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QuestionSolve the equation: 12x+32(x+1)−14=5\frac{1}{2} x+\frac{3}{2}(x+1)-\frac{1}{4}=5.

Studdy Solution

STEP 1

Assumptions1. The equation is 1x+3(x+1)−14=5\frac{1}{} x+\frac{3}{}(x+1)-\frac{1}{4}=5 . We are solving for x

STEP 2

First, distribute the 2\frac{}{2} to both terms in the parentheses.
12x+2x+2−14=5\frac{1}{2} x+\frac{}{2}x+\frac{}{2}-\frac{1}{4}=5

STEP 3

Combine like terms on the left side of the equation.
2x+32−1=52x + \frac{3}{2} - \frac{1}{} =5

STEP 4

Combine the fractions on the left side of the equation.
2x+4=2x + \frac{}{4} =

STEP 5

Subtract 54\frac{5}{4} from both sides of the equation to isolate the term with x.
2x=5−542x =5 - \frac{5}{4}

STEP 6

Convert the whole number5 to a fraction with4 as the denominator to make subtraction easier.
2x=204−542x = \frac{20}{4} - \frac{5}{4}

STEP 7

Subtract the fractions.
2x=1542x = \frac{15}{4}

STEP 8

Divide both sides of the equation by2 to solve for x.
x=154/2x = \frac{15}{4} /2

STEP 9

Convert the whole number2 to a fraction with4 as the denominator to make division easier.
x=154/84x = \frac{15}{4} / \frac{8}{4}

STEP 10

Divide the fractions.
x=158x = \frac{15}{8}So, the solution to the equation is x=158x = \frac{15}{8}.

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