6. \( 2 x-3(6-x)=4 \)

USING EQUATIONS to solve WORD PROBLEMS Directions: Set up and solve an equation for each problem below. The length of one base of a trapezoid is 19 less than five times the length of the other base. If the trapezoid has a height of 18 feet and an area of \( 477 \mathrm{ft}^{2} \), find the length of the longer base.

Two cubic roots are given below. \( \sqrt[3]{27} \) and \( \sqrt[3]{343} \) Write \( \mathrm{a} \times \mathrm{a} \times \mathrm{a} \times \mathrm{a} \times \mathrm{a} \times \mathrm{a} \) in the form of indices (b) Multiply the given two cubic roots. c) Prove that: \( \left(\frac{\mathrm{x}^{a}}{\mathrm{x}^{b}}\right)^{a+b}\left(\frac{x^{b}}{x^{c}}\right)^{b+c}\left(\frac{\mathrm{x}^{c}}{\mathrm{x}^{a}}\right)^{c+a}=1 \)

USING EQUATIONS to solve WORD PROBLEMS Directions: Set up and solve an equation for each problem below. 5. The length of a rectangle is one more than four times its width. If the perimeter of the rectangle is 62 meters, find the dimensions of the rectangle.

USING EQUATIONS to solve WORD PROBLEN Directions: Set up and solve an equation for each problem below. \( \begin{array}{l}\text { 2. Five less than twice a number is equal to one } \\ \text { half the difference of three times the number } \\ \text { and 13. Find the number. }\end{array} \)

USING EQUATIONS to solve WORD PROBLEMS Directions: Set up and solve an equation for each problem below. 1. The product of 7 and a number, increased by 3, is equal to twice the number, subtracted from 39. Find the number.