Let's break down and solve each of the given equations step-by-step.
### Part (a)
Given equation:
[tex]\[ x \cdot 3 = 5 \][/tex]
To isolate [tex]\( x \)[/tex], we need to perform the inverse operation. Since [tex]\( x \)[/tex] is multiplied by 3, we will divide both sides of the equation by 3.
[tex]\[ \frac{x \cdot 3}{3} = \frac{5}{3} \][/tex]
Simplifying the left side, the 3s cancel out, leaving:
[tex]\[ x = \frac{5}{3} \][/tex]
So the value of [tex]\( x \)[/tex] in the first equation is:
[tex]\[ x = 1.6666666666666667 \][/tex]
### Part (b)
Given equation:
[tex]\[ x \cdot 4 = 57 \][/tex]
Similarly, to isolate [tex]\( x \)[/tex], we perform the inverse operation. Since [tex]\( x \)[/tex] is multiplied by 4, we divide both sides of the equation by 4.
[tex]\[ \frac{x \cdot 4}{4} = \frac{57}{4} \][/tex]
Simplifying the left side, the 4s cancel out, leaving:
[tex]\[ x = \frac{57}{4} \][/tex]
So the value of [tex]\( x \)[/tex] in the second equation is:
[tex]\[ x = 14.25 \][/tex]
### Summary
- For [tex]\( x \cdot 3 = 5 \)[/tex], the value of [tex]\( x \)[/tex] is [tex]\( 1.6666666666666667 \)[/tex].
- For [tex]\( x \cdot 4 = 57 \)[/tex], the value of [tex]\( x \)[/tex] is [tex]\( 14.25 \)[/tex].
