1.4 Solving with fractions:Problem 5 (1 point) Multiplying both sides of th e equation 2t+(8(t-1))/(7)=4 by square we can clear the denominator and obtain the equation square =square help (formulas) This equation can be solved for t. Write you answer as a fraction. t=square help (fractions) Note: You can earn partial credit on this problem.

To solve the equation \(2t + \frac{8(t-1)}{7} = 4\), we need to clear the fraction by multiplying both sides of the equation by the denominator, which is 7.<br /><br />Step 1: Multiply both sides of the equation by 7 to clear the fraction.<br />\[ 7 \cdot \left(2t + \frac{8(t-1)}{7}\right) = 7 \cdot 4 \]<br /><br />Step 2: Simplify the equation.<br />\[ 7 \cdot 2t + 7 \cdot \frac{8(t-1)}{7} = 28 \]<br />\[ 14t + 8(t-1) = 28 \]<br /><br />Step 3: Distribute and combine like terms.<br />\[ 14t + 8t - 8 = 28 \]<br />\[ 22t - 8 = 28 \]<br /><br />Step 4: Add 8 to both sides of the equation.<br />\[ 22t - 8 + 8 = 28 + 8 \]<br />\[ 22t = 36 \]<br /><br />Step 5: Divide both sides by 22 to solve for \(t\).<br />\[ t = \frac{36}{22} \]<br />\[ t = \frac{18}{11} \]<br /><br />Therefore, the solution to the equation is:<br />\[ t = \frac{18}{11} \]