Solve the following equations for the variable: c) 5 − 24/x = 3 f) (y−3)/(y) = 2/3y − 1/2

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ScanSolve AI Tutor · Accepted Answer

c) Step 1: Subtract 5 from both sides of the equation. 5 − 24/x = 3; −24/x = 3 − 5; −24/x = −2 Step 2: Multiply both sides by x. −24 = −2x Step 3: Divide both sides by −2 to solve for x. x = (−24)/(−2); x = 12 f) Step 1: Find the least common multiple (LCM) of the denominators y, 3y, and 2. The LCM is 6y. (y−3)/(y) = 2/3y − 1/2 Step 2: Multiply every term in the equation by the LCM, 6y, to eliminate the denominators. 6y ((y−3)/(y)) = 6y (2/3y) − 6y (1/2); 6(y−3) = 2(2) − 3y(1) Step 3: Distribute and simplify the terms. 6y − 18 = 4 − 3y Step 4: Move all terms containing y to one side and constant terms to the other side. 6y + 3y = 4 + 18; 9y = 22 Step 5: Divide by 9 to solve for y. y = 22/9

Solve the following equations for the variable: c) 5 - (24)/(x) = 3 f) (y-3)/(y) = (2)/(3y) - (1)/(2)

Answers

Step-by-step solution

Part c· 3 steps

Subtract 5 from both sides of the equation.

Multiply both sides by $x$ .

Divide both sides by $-2$ to solve for $x$ .

Part f· 5 steps
$\frac{22}{9}$

Find the least common multiple (LCM) of the denominators $y$ , $3y$ , and 2.

Multiply every term in the equation by the LCM, $6y$, to eliminate the denominators.

Distribute and simplify the terms.

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

Divide by 9 to solve for $y$ .

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