Question

Rewrite the equation so that \(x\) is a function of \(y .\) Then use the result to find \(x\) when \(y=-2,-1,0,\) and 1. $$4(5-y)=14 x+3$$

Short answer

The values of \(x\) for the given \(y\) values are around 1.79 for \(y=-2\), 1.5 for \(y=-1\), 1.21 for \(y=0\), and 0.93 for \(y=1\).

Step-by-step solution

Rewrite the given equation to isolate \(x\)

Starting with the original equation \(4(5-y) = 14x + 3\), first distribute the 4 to both terms inside the parentheses which results in the equation \(20 - 4y = 14x + 3\). Then, subtract 3 from both sides to isolate \(14x\) on one side of the equation: \(17 - 4y = 14x\). Finally, divide the entire equation by 14 to solve for \(x\). The resulting equation is \(x = (17 - 4y) / 14\).

Calculate \(x\) for \(y=-2\)

Substitute \(y\) with -2 into the equation \(x = (17 - 4y) / 14\), which results in \(x = (17 - 4(-2)) / 14 = (17 + 8) / 14 = 25 / 14 = 1.79 (approximately).

Calculate \(x\) for \(y=-1\)

Substitute \(y\) with -1 into the equation \(x = (17 - 4y) / 14\), which results in \(x = (17 - 4(-1)) / 14 = (17 + 4) / 14 = 21 / 14 = 1.5.

Calculate \(x\) for \(y=0\)

Substitute \(y\) with 0 into the equation \(x = (17 - 4y) / 14\), which results in \(x = (17 - 4*0) / 14 = 17 / 14 = 1.21 (approximately).

Calculate \(x\) for \(y=1\)

Substitute \(y\) with 1 into the equation \(x = (17 - 4y) / 14\), which results in \(x = (17 - 4*1) / 14 = 13 / 14 = 0.93 (approximately).