solve an equation by combining like terms example 1 8x – 3x – 10 = 20 write original equation....
TRANSCRIPT
Solve an equation by combining like terms
EXAMPLE 1
8x – 3x – 10 = 20
8x – 3x – 10 = 20 Write original equation.
5x – 10 = 20 Combine like terms.
5x – 10 + 10 = 20 + 10 Add 10 to each side.
5x = 30 Simplify.
Divide each side by 5.
x = 6 Simplify.
= 305
5x5
Solve
EXAMPLE 2 Solve an equation using the distributive property
7x + 2(x + 6) = 39.
SOLUTION
When solving an equation, you may feel comfortable doing some steps mentally. Method 2 shows a solution where some steps are done mentally.
Solve
EXAMPLE 2
METHOD 1Show All Steps
7x + 2(x + 6) = 39
7x + 2x + 12 = 39
9x + 12 = 39
9x + 12 – 12 = 39 – 12
9x = 27
x = 3=
9x9
279
METHOD 2Do Some Steps Mentally
7x + 2(x + 6) = 39
7x + 2x + 12 = 39
9x + 12 = 39
9x = 27
x = 3
Standardized Test PracticeEXAMPLE 3
SOLUTION
ANSWER
The correct answer is D. A C DB
In Step 2, the distributive property is used to simplify the left side of the equation. Because – 4(x – 3) = – 4x+ 12, Step 2 should be 5x – 4x + 12 = 17.
Write original equation.
7d + 4 = 32 Combine like terms.
7d + 4 – 4 = 32 – 4 Subtract 4 from each side.
7d = 28 Simplify
Divide each side by 5.
d = 4 Simplify.
= 287
7d7
GUIDED PRACTICE for Examples 1, 2, and 3
9d – 2d + 4 = 321.
9d – 2d + 4 = 32
Solve the equation. Check your solution.
Check
GUIDED PRACTICE for Examples 1, 2, and 3
9d – 2d + 4 = 32 Write original equation.
Substitute 4 for d.
Multiply.
32 = 32 Simplify. Solution checks.
9(4) – 2(4) + 4 = 32?
36 – 8 + 4 = 32?
EXAMPLE 2
2w + 3w + 12 = 27
5w + 12 = 27
5w + 12 – 12 = 27 – 12
5w = 15
w = 3=
5w5
155
GUIDED PRACTICE for Examples 1, 2, and 3
2w + 3(w + 4) = 272.
2w + 3(w + 4) = 27
Solve the equation. Check your solution.
Check
GUIDED PRACTICE for Examples 1, 2, and 3
Write original equation.
Substitute 3 for w.
Multiply.
Simplify solution checks.
2w + 3(w +4) = 27
27 = 27
Simplify.
2(3) + 3(3 + 4) = 27?
6 + 21 = 27?
6 + 3(7) = 27?
EXAMPLE 2
6x – 2x + 10 = 464x + 10 = 46
4x + 10 – 10 = 46 – 10
4x = 36
x = 9=
4x4
364
GUIDED PRACTICE for Examples 1, 2, and 3
6x – 2(x – 5) = 463.
Solve the equation. Check your solution.
6x – 2(x – 5) = 46
Check
GUIDED PRACTICE for Examples1, 2, and 3
6x – 2(x – 5) = 46
46 = 46
6(9) – 2(9 – 5) = 46?
54 – 8 = 46?
54 – 2(4) = 46?