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Math

Question Solve for xx in the equation 10=43(8x+6)10=\frac{4}{3}(8x+6).

Studdy Solution

STEP 1

Assumptions
1. We are given the equation 10=43(8x+6)10 = \frac{4}{3}(8x + 6).
2. We need to solve for the variable xx.

STEP 2

First, we need to isolate the term containing xx by multiplying both sides of the equation by the reciprocal of the fraction 43\frac{4}{3}.
34×10=43×34×(8x+6)\frac{3}{4} \times 10 = \frac{4}{3} \times \frac{3}{4} \times (8x + 6)

STEP 3

Multiply the left side of the equation by 34\frac{3}{4}.
34×10=304\frac{3}{4} \times 10 = \frac{30}{4}

STEP 4

Simplify the left side of the equation.
304=7.5\frac{30}{4} = 7.5

STEP 5

On the right side, the multiplication by 43\frac{4}{3} and 34\frac{3}{4} cancels out, leaving us with the expression inside the parentheses.
7.5=8x+67.5 = 8x + 6

STEP 6

Now, we need to isolate xx by subtracting 6 from both sides of the equation.
7.5−6=8x+6−67.5 - 6 = 8x + 6 - 6

STEP 7

Simplify both sides of the equation.
1.5=8x1.5 = 8x

STEP 8

Finally, divide both sides of the equation by 8 to solve for xx.
1.58=8x8\frac{1.5}{8} = \frac{8x}{8}

STEP 9

Simplify the left side of the equation.
1.58=0.1875\frac{1.5}{8} = 0.1875

STEP 10

Simplify the right side of the equation to find the value of xx.
x=0.1875x = 0.1875
The solution to the equation 10=43(8x+6)10 = \frac{4}{3}(8x + 6) is x=0.1875x = 0.1875.

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