Solving Simple Equations

Vocabulary-style flashcards covering simplification of algebraic expressions and step-by-step solutions for linear equations from the provided lecture notes and worksheets.

Simplifying $3x + 2x + 16 - 9$

Combining like terms yields $5x + 7$.

Simplifying $-4x + 3y - 5x + 7 - 9y + 3$

Combining like terms yields $-9x - 6y + 10$.

Solving $x + 6 = 10$

Subtracting $6$ from both sides gives $x = 4$.

Solving $-7 + x = 10$

Adding $7$ to both sides gives $x = 17$.

Solving $y - 25 = 41$

Adding $25$ to both sides gives $y = 66$.

Solving $x - 4 - 4x = -1$

Combining like terms yields $-3x - 4 = -1$, which solves to $x = -1$.

Solving $3(y - 4) = 15$

Dividing both sides by $3$ yields $y - 4 = 5$, which solves to $y = 9$.

Solving $41 - 2x = 2$

Subtracting $41$ yields $-2x = -39$, which solves to $x = 19.5$.

Solving $7x + 3x = -18$

Combining like terms yields $10x = -18$, which solves to $x = -1.8$.

Solving $5x - 7x = 8$

Combining like terms yields $-2x = 8$, which solves to $x = -4$.

Solving $5 = 2x - 42 - 3x$

Combining like terms yields $5 = -x - 42$, which solves to $x = -47$.

Solving $37 = 4(7 - x)$

Distributing yields $37 = 28 - 4x$, which solves to $-4x = 9$ or $x = -2.25$.

Solving $8x + 4 - 2x = 22$

Combining like terms yields $6x + 4 = 22$, which solves to $x = 3$.

Solving $12 = 3x - x + 4x$

Combining like terms yields $12 = 6x$, which solves to $x = 2$.

Solving $-6x + 9 + 4x = -3$

Combining like terms yields $-2x + 9 = -3$, which solves to $x = 6$.

Solving $35.9 = -4x - 7.9 - 6x$

Combining like terms yields $35.9 = -10x - 7.9$, which solves to $x = -4.38$.

Solving $32 = 0.2x - 3$

Adding $3$ yields $35 = 0.2x$, which solves to $x = 175$.

Solving $8.2 + 27 + 4x + 1.8 = -45$

Combining constant terms yields $37 + 4x = -45$, which solves to $x = -20.5$.

Solving $6 - 30x - 18 = 69$

Combining constant terms yields $-12 - 30x = 69$, which solves to $x = -2.7$.

Solving $\frac{2}{3}x + 15 = 27$

Subtracting $15$ yields $\frac{2}{3}x = 12$, which solves to $x = 18$.

Solving $\frac{1}{7}x + 10 = 22$

Subtracting $10$ yields $\frac{1}{7}x = 12$, which solves to $x = 84$.

Solving $5x - 2x - 18 = 24$

Combining like terms yields $3x - 18 = 24$, which solves to $x = 14$.

Solving $6x + 4 - 8x = 28$

Combining like terms yields $-2x + 4 = 28$, which solves to $x = -12$.