Question

11x + 9 3x + 21 write an equation to solve for x : what is the value of x : enter a whole number, fraction, or decimal but do not round. what is the length of the left side of the triangle: enter a whole number, fraction, or decimal but do not round

Explanation:

Step1: Set up the equation

Since the two sides of the isosceles triangle are equal, we have \(11x + 9=3x + 21\).

Step2: Solve for \(x\)

Subtract \(3x\) from both sides: \(11x-3x + 9=3x-3x + 21\), which simplifies to \(8x+9 = 21\).
Subtract \(9\) from both sides: \(8x+9 - 9=21 - 9\), so \(8x=12\).
Divide both sides by \(8\): \(x=\frac{12}{8}=\frac{3}{2}\).

Step3: Find the length of the left - side

Substitute \(x = \frac{3}{2}\) into \(11x + 9\).
\(11\times\frac{3}{2}+9=\frac{33}{2}+9=\frac{33 + 18}{2}=\frac{51}{2}\).

Answer:

Equation: \(11x + 9=3x + 21\)
Value of \(x\): \(\frac{3}{2}\)
Length of the left - side: \(\frac{51}{2}\)