Simple Equations: 16 MCQs with answers

D · $2x + 5 = 11$

A simple equation has the unknown to the first power only, with no products of unknowns and no unknowns in denominators. $2x + 5 = 11$ fits this; the others involve a square, a denominator, or a product.

A · $ax + b = c$ with $a \neq 0$

The general form is $ax + b = c$ with $a \neq 0$, where the unknown $x$ appears only to the first power.

A · Add 3 to the right side as well

The balance model requires that whatever operation you apply to one side, you apply the same operation to the other side to keep the equation balanced.

B · Subtract 4 from both sides

Undo operations in reverse order: the last operation applied to $x$ was adding 4, so first subtract 4 from both sides to get $3x = 15$.

B · $x = 3$

Subtract 5 from both sides: $2x = 6$. Divide both sides by 2: $x = 3$. Check: $2(3) + 5 = 11$.

A · An expression has no equals sign and is simplified; an equation has an equals sign and is solved.

An expression (like $3x + 5$) has no equals sign and is simplified. An equation (like $3x + 5 = 20$) has an equals sign and is solved for the unknown.

A · True

In a simple (linear) equation in one variable, the unknown has degree exactly $1$, which is why it has exactly one solution.

A · $x = 4$

Subtract $2x$ from both sides: $3x - 3 = 9$. Add 3 to both sides: $3x = 12$. Divide by 3: $x = 4$. Check: $5(4) - 3 = 17$ and $2(4) + 9 = 17$.

B · It makes the equation messier; collecting terms first is cleaner.

Dividing by 2 is valid but often makes the equation messier. It is usually cleaner to first move all $x$-terms to one side and constants to the other, then divide.

B · $x = 12 - 7$

Transposition moves a term to the other side and flips its sign. Moving $+7$ to the right gives $-7$, so $x = 12 - 7 = 5$.

D · $2x + 7 = 19$

'Twice a number' is $2x$; 'seven more than' adds 7; 'is' signals equals. So $2x + 7 = 19$.

D · Substitute $x = 5$ into the original equation $3x + 4 = 19$

A solution is correct only if it satisfies the original equation. Substituting $x = 5$ into $3x + 4 = 19$ gives $19 = 19$, confirming it.

D · $x^2 = 9$

$x^2 = 9$ has the unknown squared, so it is not a simple (linear) equation. The others all have the unknown to the first power only.

A · $x = 16$

Expand the left side: $4x - 8 = 3x + 8$. Subtract $3x$ from both sides: $x - 8 = 8$. Add 8: $x = 16$. Check: $4(16 - 2) = 56$ and $3(16) + 8 = 56$.

A · They applied the operation to only one side, violating the balance model.

The balance model requires the same operation on both sides. Subtracting $2x$ from only the left side breaks the balance; it must be subtracted from both sides.

B · $5x - 3 = 2x + 9$

In $5x - 3 = 2x + 9$, the unknown appears on both sides. You must collect $x$-terms on one side and constants on the other before dividing.