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QuestionSolve the equation: 5t+18=t+616+t−416\frac{5 t+1}{8}=\frac{t+6}{16}+\frac{t-4}{16}.

Studdy Solution

STEP 1

Assumptions1. We are given the equation 5t+18=t+616+t−416\frac{5 t+1}{8}=\frac{t+6}{16}+\frac{t-4}{16}. . We are tasked with finding the value of tt that satisfies this equation.

STEP 2

In order to simplify the equation, we can start by multiplying the entire equation by16 to get rid of the denominators.
16⋅5t+18=16⋅t+616+16⋅t−41616 \cdot \frac{5 t+1}{8}=16 \cdot \frac{t+6}{16}+16 \cdot \frac{t-4}{16}

STEP 3

implify the equation by performing the multiplication.
2(5t+1)=t+6+t−2(5t+1)=t+6+t-

STEP 4

implify the equation further by distributing the2 on the left side of the equation and combining like terms on the right side of the equation.
10t+2=2t+210t+2=2t+2

STEP 5

Subtract 2t2t and 22 from both sides of the equation to isolate tt on one side of the equation.
10t−2t=2−210t-2t=2-2

STEP 6

implify the equation to find the value of tt.
8t=08t=0

STEP 7

Finally, divide both sides of the equation by to solve for tt.
t=0t=\frac{0}{}

STEP 8

implify to get the final solution.
t=0t=0So, the solution to the equation 5t+18=t+616+t−416\frac{5 t+1}{8}=\frac{t+6}{16}+\frac{t-4}{16} is t=0t=0.

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