Solve an equation by combining like terms

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Solve an equation by combining like terms EXAMPLE 1 Solve an equation by combining like terms Solve 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. = 30 5 5x Divide each side by 5. x = 6 Simplify.

EXAMPLE 2 Solve an equation using the distributive property Solve 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.

EXAMPLE 2 METHOD 1 METHOD 2 Do Some Steps Mentally Show All Steps 7x + 2(x + 6) = 39 7x + 2(x + 6) = 39 7x + 2x + 12 = 39 7x + 2x + 12 = 39 9x + 12 = 39 9x + 12 = 39 9x + 12 – 12 = 39 – 12 9x = 27 9x = 27 x = 3 = 9x 9 27 x = 3

EXAMPLE 3 Standardized Test Practice SOLUTION 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. ANSWER The correct answer is D. A C D B

Solve the equation. Check your solution. GUIDED PRACTICE for Examples 1, 2, and 3 Solve the equation. Check your solution. 9d – 2d + 4 = 32 1. 9d – 2d + 4 = 32 Write original equation. 7d + 4 = 32 Combine like terms. 7d + 4 – 4 = 32 – 4 Subtract 4 from each side. 7d = 28 Simplify = 28 7 7d Divide each side by 5. d = 4 Simplify.

GUIDED PRACTICE for Examples 1, 2, and 3 Check 9d – 2d + 4 = 32 Write original equation. 9(4) – 2(4) + 4 = 32 ? Substitute 4 for d. 36 – 8 + 4 = 32 ? Multiply. 32 = 32 Simplify. Solution checks.

EXAMPLE 2 GUIDED PRACTICE for Examples 1, 2, and 3 Solve the equation. Check your solution. 2w + 3(w + 4) = 27 2. 2w + 3(w + 4) = 27 2w + 3w + 12 = 27 5w + 12 = 27 5w + 12 – 12 = 27 – 12 5w = 15 = 5w 5 15 w = 3

GUIDED PRACTICE for Examples 1, 2, and 3 Check 2w + 3(w +4) = 27 Write original equation. 2(3) + 3(3 + 4) = 27 ? Substitute 3 for w. 6 + 3(7) = 27 ? Simplify. 6 + 21 = 27 ? Multiply. 27 = 27 Simplify solution checks.

EXAMPLE 2 GUIDED PRACTICE for Examples 1, 2, and 3 Solve the equation. Check your solution. 6x – 2(x – 5) = 46 3. 6x – 2(x – 5) = 46 6x – 2x + 10 = 46 4x + 10 = 46 4x + 10 – 10 = 46 – 10 4x = 36 = 4x 4 36 x = 9

GUIDED PRACTICE for Examples1, 2, and 3 Check 6x – 2(x – 5) = 46 6(9) – 2(9 – 5) = 46 ? 54 – 2(4) = 46 ? 54 – 8 = 46 ? 46 = 46