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Solve an equation using addition
EXAMPLE 2
Solve x – 12 = 3.
Horizontal format Vertical format
x– 12 = 3 Write original equation. x – 12 = 3
Add 12 to each side. +12 +12
x = 15 Simplify. x = 15
x – 12 + 12 = 3 +12
Solve an equation using division
EXAMPLE 3
Solve – 6x = 48.
– 6x = 48
x = – 8
Write original equation.
– 6x– 6
48– 6= Divide each side by – 6.
Simplify.
GUIDED PRACTICE for Example 2 and 3
1. y + 7 = 10.
y + 7 = 10 Write original equation.
y + 7 – 7 = 10 – 7 Use subtraction property of equality: Subtract 7 from each side.
y = 3 Simplify.
ANSWERThe solution is 3.
Solve the equation. Check your solution.
GUIDED PRACTICE for Example 2 and 3
CHECK Substitute 3 for y in the original equation.
y + 7 = 10Write original equation.
3 + 7 = 10? Substitute 3 for y.
10 = 10 Simplify. Solution checks.
2. x – 5 = 3.
Horizontal format Vertical format
x – 5 = 3 Write original equation. x – 5 = 3
Add 5 to each side. +5 +5
x = 8 Simplify. x = 8
x – 5 + 5 = 3 +5
GUIDED PRACTICE for Example 2 and 3
Solve the equation. Check your solution.
GUIDED PRACTICE for Example 2 and 3
CHECK Substitute 8 for x in the original equation.
x – 5 = 3 Write original equation.
8 – 5 = 3? Substitute 8 for x.
3 = 3 Simplify. Solution checks.
GUIDED PRACTICE for Example 2 and 3
3. q – 11 = – 5.
Horizontal format Vertical format
q – 11 = – 5 Write original equation. q – 11 = – 5
Add 11 to each side.
q = 6 Simplify. q = 6
q – 11 + 11 = – 5 +11 +11– 11
Solve the equation. Check your solution.
GUIDED PRACTICE for Example 2 and 3
CHECK Substitute 6 for q in the original equation.
q – 11 = –5 Write original equation.
6 – 11 = –5? Substitute 6 for q.
–5 = –5 Simplify. Solution checks.
GUIDED PRACTICE for Example 2 and 3
4. 6 = t – 2.
Horizontal format Vertical format
6 = t – 2 Write original equation. 6 = t – 2
Add 2 to each side. + 2 + 2
8 = t Simplify. 8 = t
6 + 2 = t – 2 + 2
Solve the equation. Check your solution.
GUIDED PRACTICE for Example 2 and 3
CHECK Substitute 8 for t in the original equation.
6 = t – 2 Write original equation.
6 = 8 – 2? Substitute 8 for t.
6 = 6 Simplify. Solution checks.
GUIDED PRACTICE for Example 2 and 3
5. 4x = 48.
4x = 48
x = 12
Write original equation.
4x 4
48 4= Divide each side by 4.
Simplify.
Solve the equation. Check your solution.
GUIDED PRACTICE for Example 2 and 3
CHECK Substitute 12 for x in the original equation.
4x = 48. Write original equation.
Substitute 12 for x.
48 = 48 Simplify. Solution checks.
4 12 = 48?
GUIDED PRACTICE for Example 2 and 3
6. – 65 = – 5y.
– 65 = – 5y
13 = y
Write original equation.
– 65– 5
– 5y– 5= Divide each side by – 5s
Simplify.
Solve the equation. Check your solution.
GUIDED PRACTICE for Example 2 and 3
CHECK Substitute 13 for y in the original equation.
– 65 = – 5y Write original equation.
Substitute 13 for y.
– 65 = – 65 Simplify. Solution checks.
– 65 = – 5? 13
GUIDED PRACTICE for Example 2 and 3
7. 6w = – 54.
6w = – 54
w = – 9
Write original equation.
6w 6
– 54 6= Divide each side by 6.
Simplify.
Solve the equation. Check your solution.
GUIDED PRACTICE for Example 2 and 3
CHECK Substitute 9 for w in the original equation.
6w = – 54 Write original equation.
Substitute – 9 for w.
– 54 = – 54 Simplify. Solution checks.
6 – 9 = – 54?
GUIDED PRACTICE for Example 2 and 3
8. 24 = – 8n.
24 = – 8n
– 3 = n
Write original equation.
24– 8
– 8n– 8= Divide each side by – 8.
Simplify.
Solve the equation. Check your solution.
GUIDED PRACTICE for Example 2 and 3
CHECK Substitute – 3 for n in the original equation.
24 = – 8n Write original equation.
Substitute – 3 for n.
24 = 24 Simplify. Solution checks.
24 = – 8? – 3
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