Multiplying both sides by 3: $2x = 18 \times 3 = 54$ $x = \frac{54}{2} = 27$.

Question 1

What is the degree of a linear equation in one variable?

Accepted Answer

A linear equation in one variable is an equation in which the highest power (degree) of the variable present in the equation is 1.

Question 2

Solve for $x$: $\frac{2x}{3} = 18$

Accepted Answer

Multiplying both sides by 3: $2x = 18 	imes 3 = 54$ $x = \frac{54}{2} = 27$.

Question 3

Solve: $3x = 2x + 18$

Accepted Answer

Transposing $2x$ to LHS: $3x - 2x = 18$ $x = 18$.

Question 4

Solve: $8x + 4 = 3(x - 1) + 7$

Accepted Answer

Expanding RHS: $8x + 4 = 3x - 3 + 7$ $8x + 4 = 3x + 4$ $8x - 3x = 4 - 4$ $5x = 0 \implies x = 0$.

Question 5

Two numbers are in the ratio $5:3$. If they differ by $18$, what are the numbers?

Accepted Answer

Let the numbers be $5x$ and $3x$. $5x - 3x = 18 \implies 2x = 18 \implies x = 9$.
Numbers are $5(9) = 45$ and $3(9) = 27$.

Linear Equations in One Variable