Question

solve the equation (7(x + 1) = 6(x + 9))
a. apply the distribution property.
b. use the addition property to get the variable term on the left side of the equation.
c. use the addition property to isolate the variable term on one side of the equation.
d. check the solution.
a. apply the distributive property.
(7(x + 1) = 6(x + 9))
(7x + 7 = 6x + 54)
(simplify your answer. type the terms of your expression in the same order as they appear in...)
b. use the addition property to get the variable term on the left side of the equation.
(7x + 7 = 6x + 54)
(-6x) (-6x)
(1x + 7 = 0x + 54) subtract
(1x + 7 = 54) simplify
c. use the addition property to isolate the variable term on one side of the equation.
(x + 7 = 54)
(-7) (-7)
(x + 0 = 47) subtract
(x = 47) simplify
d. check the solution
(7(47 + 1) stackrel{?}{=} 6(47 + 9)) substitute
(7(square) stackrel{?}{=} 6(square)) add

Explanation:

Step1: Calculate inside the parentheses for left side

First, calculate \(47 + 1\) which equals \(48\).

Step2: Calculate inside the parentheses for right side

Next, calculate \(47 + 9\) which equals \(56\).

Answer:

For the left - hand side box, we put \(48\) (since \(47 + 1=48\)) and for the right - hand side box, we put \(56\) (since \(47 + 9 = 56\)). So the equation becomes \(7(48)=6(56)\), and we can further check: \(7\times48 = 336\) and \(6\times56=336\), which confirms the solution is correct. The values to fill in the boxes are \(48\) (left) and \(56\) (right).