Solving Linear Equations Practice

Vocabulary-style flashcards providing full solutions and classifications for the algebra equations shown in the practice image.

Solving an Equation Practice Set

A set of linear equations (problems 22 through 33) to solve for $x$ and check solutions, determining whether each equation has one solution, no solution, or infinitely many solutions.

Equation 22: $x + 6 = x$

The equation has no solution because subtracting $x$ from both sides results in the false statement $6 = 0$.

Equation 23: $3x - 1 = 1 - 3x$

The solution is $x = \frac{1}{3}$, obtained by adding $3x$ and $1$ to both sides to get $6x = 2$.

Equation 24: $3x + 15 = 3(x + 5)$

The equation has infinitely many solutions because distributing on the right side yields the identity $3x + 15 = 3x + 15$.

Equation 25: $4x - 9 = 3.5x - 9$

The solution is $x = 0$, obtained by adding $9$ to both sides and subtracting $3.5x$ to get $0.5x = 0$.

Equation 26: $\frac{1}{3}(9x + 3) = 3x + 1$

The equation has infinitely many solutions because distributing $\frac{1}{3}$ yields the identity $3x + 1 = 3x + 1$.

Equation 27: $5x - 7 = 4x - 1$

The solution is $x = 6$, obtained by subtracting $4x$ and adding $7$ to both sides.

Equation 28: $\frac{1}{2}x + \frac{1}{2}x = x + 1$

The equation has no solution because combining like terms yields $x = x + 1$, which simplifies to the false statement $0 = 1$.

Equation 29: $2x + 4 = -(-7x + 4)$

The solution is $x = \frac{8}{5}$, obtained by simplifying the right side to $7x - 4$ and solving $2x + 4 = 7x - 4$.

Equation 30: $5.5 - x = -4.5 - x$

The equation has no solution because adding $x$ to both sides leads to the false statement $5.5 = -4.5$.

Equation 31: $-3(2x - 3) = -6x + 9$

The equation has infinitely many solutions because distributing $-3$ on the left side yields the identity $-6x + 9 = -6x + 9$.

Equation 32: $10x - \frac{8}{3} - 4x = 6x$

The equation has no solution because combining terms on the left yields $6x - \frac{8}{3} = 6x$, which simplifies to the false statement $-\frac{8}{3} = 0$.

Equation 33: $6(7x + 7) = 7(6x + 6)$

The equation has infinitely many solutions because distributing both sides yields the identity $42x + 42 = 42x + 42$.