Question 1 of 5

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.

Solve the following equation for [tex]$x$[/tex], and express its value in terms of [tex]$c$[/tex].
[tex]
3(cx - 7) = 9
[/tex]

The value of [tex]$x$[/tex] in the equation is [tex] \boxed{\ } \]



Answer :

To solve the equation [tex]\( 3(c x - 7) = 9 \)[/tex] for [tex]\( x \)[/tex], follow these steps:

1. Distribute the 3 on the left-hand side of the equation:

[tex]\[ 3(c x - 7) = 3 \cdot (c x) - 3 \cdot 7 = 3 c x - 21 \][/tex]

Thus the equation becomes:

[tex]\[ 3 c x - 21 = 9 \][/tex]

2. Isolate the term with [tex]\( x \)[/tex]. To do this, first add 21 to both sides of the equation to move the constant term:

[tex]\[ 3 c x - 21 + 21 = 9 + 21 \][/tex]

[tex]\[ 3 c x = 30 \][/tex]

3. Solve for [tex]\( x \)[/tex] by dividing both sides of the equation by [tex]\( 3c \)[/tex]:

[tex]\[ x = \frac{30}{3 c} = \frac{10}{c} \][/tex]

So, the value of [tex]\( x \)[/tex] in the equation is [tex]\( \frac{10}{c} \)[/tex].