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Math  /  Algebra

QuestionSolve the following equation: 34x=60\frac{3}{4} x=60

Studdy Solution

STEP 1

1. The equation 34x=60\frac{3}{4} x = 60 is asking us to solve for xx.
2. This is a one-step equation involving a fraction.
3. The equation involves basic algebraic operations, specifically multiplication and division.

STEP 2

1. Understand the equation and what it represents.
2. Isolate the variable xx by performing algebraic operations.
3. Verify the solution by substituting it back into the original equation.

STEP 3

The equation 34x=60\frac{3}{4} x = 60 means that 34\frac{3}{4} times some value xx equals 60.

STEP 4

To solve for xx, we need to eliminate the fraction. We do this by multiplying both sides of the equation by the reciprocal of 34\frac{3}{4}, which is 43\frac{4}{3}:
43×34x=43×60 \frac{4}{3} \times \frac{3}{4} x = \frac{4}{3} \times 60

STEP 5

Simplify the left side of the equation:
x=43×60 x = \frac{4}{3} \times 60
Calculate the right side:
x=2403 x = \frac{240}{3}
x=80 x = 80

STEP 6

Verify the solution by substituting x=80x = 80 back into the original equation:
34×80=60 \frac{3}{4} \times 80 = 60

STEP 7

Simplify the left side:
2404=60 \frac{240}{4} = 60
Since both sides are equal, the solution is verified.
Therefore, the solution is:
80 \boxed{80}

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