Solve the inequality: 1/3(2x+5) + 3/2(x−1) 3(x+1)

Question

ScanSolve AI Tutor · Accepted Answer

Step 1: Write down the inequality. 1/3(2x+5) + 3/2(x−1) ≥ 3(x+1) Step 2: Multiply both sides of the inequality by the least common multiple (LCM) of the denominators (3 and 2), which is 6, to eliminate the fractions. 6 ( 1/3(2x+5) + 3/2(x−1) ) ≥ 6 ( 3(x+1) ) 2(2x+5) + 9(x−1) ≥ 18(x+1) Step 3: Distribute the numbers into the parentheses on both sides. (2 × 2x) + (2 × 5) + (9 × x) + (9 × −1) ≥ (18 × x) + (18 × 1) 4x + 10 + 9x − 9 ≥ 18x + 18 Step 4: Combine like terms on the left side of the inequality. (4x + 9x) + (10 − 9) ≥ 18x + 18 13x + 1 ≥ 18x + 18 Step 5: Move all terms containing x to one side and constant terms to the other side. Subtract 13x from both sides. 1 ≥ 18x − 13x + 18 1 ≥ 5x + 18 Step 6: Subtract 18 from both sides. 1 − 18 ≥ 5x −17 ≥ 5x Step 7: Divide both sides by 5 to solve for x. (−17)/(5) ≥ x This can also be written as: x ≤ −17/5 The final answer is x ≤ −17/5.

Solve the inequality: (1)/(3)(2x+5) + (3)/(2)(x-1) 3(x+1)

Answer

Step-by-step solution

Write down the inequality.

Multiply both sides of the inequality by the least common multiple (LCM) of the denominators (3 and 2), which is 6, to eliminate the fractions.

Distribute the numbers into the parentheses on both sides.

Combine like terms on the left side of the inequality.

Move all terms containing $x$ to one side and constant terms to the other side.

Subtract 18 from both sides.

Divide both sides by 5 to solve for $x$ .

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