Page 159 - Math Course 1 (Book 1)

Equations with Grouping Symbols

8w + 4 – 4 = 36 – 4 Subtract 4 from each side. Your Turn!

8w = 32 Simplify. Use an Equation to Solve a Problem

w = 4 Mentally divide each side GEOMETRY
by 8. The perimeter of a rectangle is 26 feet. Find the
dimensions if the length is 2 feet less than twice
Evaluate 3w + 2 to f nd the length. the width.
3(4) + 2 = 12 + 2 or 14 Replace w with 4. 2 1
A. width = 3 ft ; length = 5 ft
3 3
2
1
The width is 4 inches. B. width = 4 ft ; length = 7 ft
Answer
The length is 14 inches. 3 3
C. width = 5 ft; length = 8 ft
No Solution D. width = 11 ft; length = 24 ft

Answer
Example

Solve 4x – 0.3 = 4x + 0.9.

4x – 0.3 = 4x + 0.9 Write the equation.

4x – 4x – 0.3 = 4x – 4x + 0.9 Subtract 4x from
each side.

–0.3 = 0.9 Simplify.

The sentence –0.3 = 0.9 is never
Answer true. So, the solution set is Ø.

All Numbers as Solutions

No Solution
Example Solve 16 + 1.3m = –12 + 1.3m.

Solve 3(4x – 2) + 15 = 12x + 9. A. 3.1
B. 21.5
3(4x – 2) + 15 = 12x + 9 Write the equation. C. The solution set is Ø.
D. The solution set is all numbers.
12x – 6 + 15 = 12x + 9 Use the Distributive
Property.
Answer
12x + 9 = 12x + 9 Simplify.

12x + 9 – 9 = 12x + 9 – 9 Subtract 9 from each
side.

12x = 12x Simplify.

x = x Mentally divide each
side by 12.

The sentence x = x is always true.
Answer The solution set is all numbers.

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