Solving One & Two Step Equations with the variable on 1 ...
Transcript of Solving One & Two Step Equations with the variable on 1 ...
Solving One & Two Step Equations with the variable on 1 side[Algebra 1 InClass Notes].notebook
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October 07, 2017
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Homework Assignment
The following examples have to be copied for next class
Example 1
The examples must be copied and ready for me to check once you come to class.
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
Example 10
Example 11
Solving One & Two Step Equations with the variable on 1 side[Algebra 1 InClass Notes].notebook
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Steps to solving a linear equation.
If possible simplify each side of the equation removing grouping symbols.
If possible, combine like terms(MUST to be on the same side of the equation).
If the variable that you want to solve for is on both sides of the equation cancel out one of the variables.
Add (or subtract) the same real number or variable expression on both sides of the equation.
Multiply (or divide) by the same nonzero number on both sides of the equation.
1.
2.
3.
4.
5.
Solving One & Two Step Equations with the variable on 1 side[Algebra 1 InClass Notes].notebook
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EXAMPLE 1
Solve :
SOLUTION
–2 + x = –7
–2 + x = –7
x = –5
–2 + x = –7 +2 +2
Solving One & Two Step Equations with the variable on 1 side[Algebra 1 InClass Notes].notebook
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Verify that the solution is correct.
–2 + x = –7
Substitute –5 in for x, simplify and check that both sides of the equation are equal.
–2 + (–5) = –7
–2 – 5 = –7 –7 = –7
x = –5 does satisfy the equation.
Solving One & Two Step Equations with the variable on 1 side[Algebra 1 InClass Notes].notebook
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EXAMPLE 2
Solve :
SOLUTION
32= –6 + x + 11
9 = x + 5
32= –6 + x + 11
9 = x + 5
9 = x + 5 – 5 – 5
4 = x
Solving One & Two Step Equations with the variable on 1 side[Algebra 1 InClass Notes].notebook
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October 07, 2017
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Verify that the solution is correct.
Substitute 4 in for x, simplify and check that both sides of the equation are equal.
x = 4, does satisfy the equation.
9 = x + 5 9 = 4 + 5
9 = 9
Solving One & Two Step Equations with the variable on 1 side[Algebra 1 InClass Notes].notebook
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October 07, 2017
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EXAMPLE 3
Solve :
SOLUTION
Simplify each side of the equation, if possible.
x4 = 3
2 – 7 2
x4 = 9
– 7 2
x4 = 9
– 14
x4 =
–5
Solving One & Two Step Equations with the variable on 1 side[Algebra 1 InClass Notes].notebook
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x4 4 = –5 4
x4 4 = –20
x = –20
x4 =
–5
Solving One & Two Step Equations with the variable on 1 side[Algebra 1 InClass Notes].notebook
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EXAMPLE 4
Solve :
SOLUTION
18 9 – 8 = –3x
2 – 8 = –3x–6 = –3x
–6 = –3x
–6 = –3x–3 –3–6 = –3x–3 –3
2 = x
Solving One & Two Step Equations with the variable on 1 side[Algebra 1 InClass Notes].notebook
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EXAMPLE 5
Solve :
SOLUTION
x = 623
x = 623
Solving One & Two Step Equations with the variable on 1 side[Algebra 1 InClass Notes].notebook
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Option 1Multiply both sides of the equation by the reciprocal of the fraction.
x = 623
x = 623
32
32
x = 66
312
x =23
32
32
16
x = 4
Solving One & Two Step Equations with the variable on 1 side[Algebra 1 InClass Notes].notebook
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Option 2Eliminate the fraction by multiplying both sides of the equation by denominator.
After the fraction is eliminated use the appropriate steps to solve the equation.
x = 623
3x =12
x = 2 6232
x = 12232
Solving One & Two Step Equations with the variable on 1 side[Algebra 1 InClass Notes].notebook
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33x
312=
33x
312=
x = 4
Solving One & Two Step Equations with the variable on 1 side[Algebra 1 InClass Notes].notebook
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EXAMPLE 6
Solve :
SOLUTION
Simplify each side of the equation, if possible.
9x + 8 – 7x – 13= –11
9x + 8 – 7x – 13= –11
2x – 5= –11
2x – 5 = –11
Solving One & Two Step Equations with the variable on 1 side[Algebra 1 InClass Notes].notebook
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2x – 5= –11+
5 +
52x = –6
2x = –62 2
2x = –62 2x = –3
Solving One & Two Step Equations with the variable on 1 side[Algebra 1 InClass Notes].notebook
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EXAMPLE 7
Solve :
SOLUTION
17 = 9x + 2(–7x + 8) – 4
17 = 9x + 2(–7x + 8) – 4
17 = 9x – 14x +16 – 4
17 = –5x +12
17 = –5x +12
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17 = –5x +12–12 –125 = –5x 5 –5x
–5–5 =
5 –5x –5–5 =
–1= x
Solving One & Two Step Equations with the variable on 1 side[Algebra 1 InClass Notes].notebook
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EXAMPLE 8
Solve :
SOLUTIONPlace a 1 in front of the parentheses then distribute –1 to each of the terms.
–9 – (3x – 4) + 2x = – 11
–9 – 1(3x – 4) + 2x = – 11
–9 – 1(3x – 4) + 2x = – 11
–9 – 3x + 4 + 2x = – 11
–5 – 1x = – 11
Solving One & Two Step Equations with the variable on 1 side[Algebra 1 InClass Notes].notebook
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–5 – 1x = – 11+ 5 + 5
–1x = – 6
–1x – 6–1 –1=
–1x – 6= –1 –1
x = 6
Solving One & Two Step Equations with the variable on 1 side[Algebra 1 InClass Notes].notebook
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EXAMPLE 9
Solve :
SOLUTION
Place a 1 in front of any variable that does not have a coefficient and in front of the parentheses then distribute –1 to each of the terms.
–7x – (–6x + 5) + x = – 5
–7x – 1(–6x + 5) + 1x = – 5
–7x – 1(–6x + 5) + 1x = – 5
–7x + 6x – 5 + 1x = – 5
Solving One & Two Step Equations with the variable on 1 side[Algebra 1 InClass Notes].notebook
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–5 + 0x = – 5–5 + 0 = – 5
–5 = – 5
This equation is a special case when solving linear equations where the variable cancels out and only numbers remain. Whenever this happens your answer will be one of two choices.
If the equation is TRUE, where both sides of the equation are equal the solution is.
ALL REAL NUMBERS
Option 1
Solving One & Two Step Equations with the variable on 1 side[Algebra 1 InClass Notes].notebook
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If the equation is FALSE, where both sides of the equation are NOT equal , the solution is.
NO SOLUTION
Option 2
Solving One & Two Step Equations with the variable on 1 side[Algebra 1 InClass Notes].notebook
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EXAMPLE 10
Solve :
SOLUTION
x + 4 – x = 632
37
Eliminate all fractions in the equation by multiplying the entire equation by the least common multiple of all the denominators.
Solving One & Two Step Equations with the variable on 1 side[Algebra 1 InClass Notes].notebook
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x + 4 – x = 632
37
– x + 4 = 635
Option 1
– x + 4 = 635
Add or subtract the fractions that are like terms solve the equation from that point using the appropriate steps.
– x + 4 = 635
– 4 – 4
– x = 235
Solving One & Two Step Equations with the variable on 1 side[Algebra 1 InClass Notes].notebook
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– x = 235
53– 5
3–
– x =35
53– 5
3– 12
x =15 – 56
15
x = – 56
Multiply by the reciprocal of the coefficient to isolate the x variable.
Solving One & Two Step Equations with the variable on 1 side[Algebra 1 InClass Notes].notebook
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Eliminate all fractions in the equation by multiplying the entire equation by the least common multiple of all the denominators.
Option 2
x + 4 – x = 632
37
Both denominators are the number 3 so the least common multiple is also 3.
Multiply the entire equation by 3.
x + 4 – x = 632
373( )
x + 4 – x = 632
373( )
Solving One & Two Step Equations with the variable on 1 side[Algebra 1 InClass Notes].notebook
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October 07, 2017
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x + 4 – x = 632
373 3 3 3
2x +12 – 7x = 18
x + 4 – x = 632
373 3 3 3
–5x +12 = 18–12 –12–5x =
6
Solving One & Two Step Equations with the variable on 1 side[Algebra 1 InClass Notes].notebook
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October 07, 2017
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–5x 6–5 –5 =
–5x 6–5 –5 =
x = –
65
Solving One & Two Step Equations with the variable on 1 side[Algebra 1 InClass Notes].notebook
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EXAMPLE 11
Solve :
SOLUTION
x – 1
+ x =37
25–
38–
Both denominators are the numbers 2 & 3 so the least common multiple is 6.
Multiply the entire equation by 6.
6( )x – 1
+ x =37
25–
38–
x – 1
+
x =
37
25– 3
8–6 6 6 6
Solving One & Two Step Equations with the variable on 1 side[Algebra 1 InClass Notes].notebook
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October 07, 2017
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–15x – 6
+ 14x = –16
–1x – 6
= –16
x – 1
+
x =
37
25– 3
8–6 6 6 623 2
3 5x – 1
+ 7777
x =– 8–6 2 2
–1x – 6
= –16