To solve the equation [tex]\( 7x + 3 = 52 \)[/tex], we need to isolate the variable [tex]\( x \)[/tex]. Here is a step-by-step explanation of each step involved in solving this equation:
1. Original Equation:
[tex]\[
7x + 3 = 52
\][/tex]
We start with the given equation where [tex]\( 7x \)[/tex] is multiplied by 7 and then 3 is added.
2. Isolate the variable term by subtracting 3 from both sides:
[tex]\[
7x + 3 - 3 = 52 - 3
\][/tex]
Subtract 3 from both sides of the equation to move the constant term on the left side to the right side. This helps in isolating the variable term [tex]\( 7x \)[/tex] on the left side of the equation.
3. Simplify both sides:
[tex]\[
7x = 49
\][/tex]
After performing the subtraction, we get [tex]\( 7x \)[/tex] on the left side and [tex]\( 49 \)[/tex] on the right side. Now, we have an equation with the variable term [tex]\( 7x \)[/tex] isolated.
4. Isolate the variable by dividing both sides by 7:
[tex]\[
\frac{7x}{7} = \frac{49}{7}
\][/tex]
Divide both sides of the equation by the coefficient of [tex]\( x \)[/tex] (which is 7) to solve for [tex]\( x \)[/tex]. This step helps to isolate the variable [tex]\( x \)[/tex] by removing the coefficient.
5. Simplify both sides:
[tex]\[
x = 7
\][/tex]
Simplify the division to find the value of [tex]\( x \)[/tex]. The solution to the equation is [tex]\( x = 7 \)[/tex].
By following these steps, we successfully isolate the variable [tex]\( x \)[/tex] and solve the equation to find that [tex]\( x = 7 \)[/tex].
