Solve the following equation: (1+4x)/2 − (5+2x)/7 = x−2

Question

ScanSolve AI Tutor · Accepted Answer

Here's how to solve the equation: Step 1: Write the given equation. (1+4x)/(2) − (5+2x)/(7) = x−2 Step 2: Find a common denominator for the fractions on the left side. The least common multiple of 2 and 7 is 14. (7(1+4x))/(14) − (2(5+2x))/(14) = x−2 Step 3: Combine the fractions on the left side. (7(1+4x) − 2(5+2x))/(14) = x−2 Step 4: Distribute the numbers in the numerator. (7 + 28x − 10 − 4x)/(14) = x−2 Step 5: Combine like terms in the numerator. (24x − 3)/(14) = x−2 Step 6: Multiply both sides by 14 to eliminate the denominator. 24x − 3 = 14(x−2) Step 7: Distribute 14 on the right side. 24x − 3 = 14x − 28 Step 8: Move all terms with x to one side and constant terms to the other side. Subtract 14x from both sides. 24x − 14x − 3 = −28; 10x − 3 = −28 Step 9: Add 3 to both sides. 10x = −28 + 3; 10x = −25 Step 10: Divide by 10 to solve for x. x = (−25)/(10); x = −5/2 The final answer is −5/2.

Solve the following equation: (1+4x)/2 - (5+2x)/7 = x−2

Answer

Step-by-step solution

Write the given equation.

Find a common denominator for the fractions on the left side.

Combine the fractions on the left side.

Distribute the numbers in the numerator.

Combine like terms in the numerator.

Multiply both sides by 14 to eliminate the denominator.

Distribute 14 on the right side.

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

Add 3 to both sides.

Divide by 10 to solve for $x$ .

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