Question

name date class
lesson 11 - 2
addition and subtraction equations
practice and problem solving: a/b
solve each equation. graph the solution on the number line.

1. ( 6 = r + 2 ) ( r=)___
2. ( 26 = w - 12 ) ( w=)___
3. ( \frac{1}{2}=m-\frac{1}{8} ) ( m=)___
4. ( t + 1=-3 ) ( t=)___

use the drawing at the right for exercises 5 - 6.

1. write an equation to represent the measures of the angles.

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1. solve the equation to find the measure of the unknown angle.

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use the drawing at the right for exercises 7 - 8.

1. write an equation to represent the measures of the angles.

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1. solve the equation to find the measure of the unknown angle.

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write a problem for the equation ( 3 + x = 8 ). then solve the equation and write the answer to your problem.
9.___
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Explanation:

Step1: Solve equation \(6 = r + 2\)

Subtract 2 from both sides: \(r=6 - 2\)

Step2: Solve equation \(26=w - 12\)

Add 12 to both sides: \(w = 26+12\)

Step3: Solve equation \(\frac{1}{2}=m-\frac{1}{8}\)

Add \(\frac{1}{8}\) to both sides: \(m=\frac{1}{2}+\frac{1}{8}=\frac{4 + 1}{8}=\frac{5}{8}\)

Step4: Solve equation \(t + 1=-3\)

Subtract 1 from both sides: \(t=-3 - 1\)

Step5: For the first angle - pair (supplementary angles)

Since \(x\) and \(139^{\circ}\) are supplementary (\(x + 139=180\))

Step6: Solve \(x + 139=180\)

Subtract 139 from both sides: \(x=180 - 139\)

Step7: For the second angle - pair (complementary angles)

Since \(x\) and \(18^{\circ}\) are complementary (\(x+18 = 90\))

Step8: Solve \(x + 18=90\)

Subtract 18 from both sides: \(x=90 - 18\)

Step9: For the equation \(3 + x=8\)

Problem: There are 3 red apples and \(x\) green apples in a basket. The total number of apples is 8. How many green apples are there?
Solve: Subtract 3 from both sides \(x=8 - 3\)

Answer:

1. \(r = 4\)
2. \(w=38\)
3. \(m=\frac{5}{8}\)
4. \(t=-4\)
5. \(x + 139=180\)
6. \(x = 41^{\circ}\)
7. \(x+18 = 90\)
8. \(x = 72^{\circ}\)
9. Problem: There are 3 red apples and \(x\) green apples in a basket. The total number of apples is 8. How many green apples are there? Solution: \(x=5\)