Question

Solve each of the following for x: $(1.4)$

a. $2x+5=41$

b.$\frac{5x}{3}=40$

Short answer

a. The value of x is$18$.

b. The value of x is$24$.

Step-by-step solution

Part (a) step 1: Given Information

We need to find the value of $x$from given equation $2x+5=41$.

Part (a) step 2: Calculation

Consider:

$2x+5=41$

Now, we contain variable$x$on one side:

role="math" localid="1651834633013" $$\begin{gathered} 2x=41-5 \\ 2x=36 \end{gathered}$$

Both sides divide by $2$:

$\frac{2x}{2}=\frac{36}{2}$

$x=18$

Part (b) step 1: Given Information

We need to find the value of$x$ from given equation$\frac{5x}{3}=40$.

Part (b) step 2: Calculation

Consider :

$\frac{5x}{3}=40$

Now,

we cross-multiplication by multiplying $5x$to $1$and $40$to $3$.

Therefore:

$$\begin{gathered} \left(5x\right)\left(1\right)=\left(40\right)\left(3\right) \\ 5x=120 \end{gathered}$$

Now, both sides are divided by $5$.

So,

$$\begin{gathered} \frac{5x}{5}=\frac{120}{5} \\ x=24 \end{gathered}$$