Qrs is an equilateral triangle. If QR is seven less than twice x, RS is 61 less than 5 times x, and QS is 11 more than x, find x and the measure of each side

x = 18 and the length of each side of the triangle is 29. This is a matter of reading the descriptions and converting to mathematical notation. "QRS is an equilateral triangle" We now know that all three sides of the triangle have the same length. "If QR is seven less than twice x". So we can write QR = 2x - 7 "RS is 61 less than 5 times x". So we can write RS = 5x - 61 "QS is 11 more than x". And we can write QS = x + 11 And because we already know that they all have the same length, then we can set those equations equal to each other. Let's just pick 2 of them. Will use the length of QR and QS because they look the simplest and then will solve for x. QR = 2x - 7 RS = 5x - 61 QS = x + 11 2x - 7 = x + 11 x - 7 = 11 x = 18 So we now know that x = 18. Let's check to make sure all three equations have the same value. QR = 2x - 7 = 2*18 - 7 = 36 - 7 = 29 RS = 5x - 61 = 5*18 - 61 = 90 - 61 = 29 QS = x + 11 = 18 + 11 = 29 And they all are equal, so 18 is the correct value for x.