Solve the linear equations and check the solution. a) 10x−1=15−6x b) 3x/2 + 5 = 5x/2 −1

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ScanSolve AI Tutor · Accepted Answer

Here are the solutions for the linear equations: a) Solve 10x − 1 = 15 − 6x Step 1: Add 6x to both sides of the equation. 10x − 1 + 6x = 15 − 6x + 6x; 16x − 1 = 15 Step 2: Add 1 to both sides of the equation. 16x − 1 + 1 = 15 + 1; 16x = 16 Step 3: Divide both sides by 16. 16x/16 = 16/16; x = 1; Step 4: Check the solution by substituting x=1 into the original equation. 10(1) − 1 = 15 − 6(1); 10 − 1 = 15 − 6; 9 = 9 The solution is correct. The solution for a) is x=1. b) Solve 3x/2 + 5 = 5x/2 − 1 Step 1: Multiply the entire equation by 2 to eliminate the denominators. 2 (3x/2 + 5) = 2 (5x/2 − 1); 3x + 10 = 5x − 2 Step 2: Subtract 3x from both sides of the equation. 3x + 10 − 3x = 5x − 2 − 3x; 10 = 2x − 2 Step 3: Add 2 to both sides of the equation. 10 + 2 = 2x − 2 + 2; 12 = 2x Step 4: Divide both sides by 2. 12/2 = 2x/2; 6 = x; Step 5: Check the solution by substituting x=6 into the original equation. (3(6))/(2) + 5 = (5(6))/(2) − 1; 18/2 + 5 = 30/2 − 1; 9 + 5 = 15 − 1; 14 = 14 The solution is correct. The solution for b) is x=6.

Solve the linear equations and check the solution. a) 10x−1=15−6x b) 3x/2 + 5 = 5x/2 -1

Answers

Step-by-step solution

Part a· 4 steps

Add $6x$ to both sides of the equation.

Add 1 to both sides of the equation.

Divide both sides by 16.

Check the solution by substituting $x=1$ into the original equation.

Part b· 5 steps
$x=6$

Multiply the entire equation by 2 to eliminate the denominators.

Subtract $3x$ from both sides of the equation.

Add 2 to both sides of the equation.

Divide both sides by 2.

Check the solution by substituting $x=6$ into the original equation.

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