Back to Exercise: Solve linear equations and inequalities

Exercises: Solving Linear Equations and Inequalities in One Variable

Show all steps. For inequalities, express your answer in inequality notation unless a different form is requested.

Grade 9·23 problems·~30 min·Common Core Math - HS Algebra·standard·hsa-rei-b-3

Work through problems with immediate feedback

Warm-Up: Review What You Know

These problems review skills from earlier courses.

Which value of $x$ satisfies $2x + 6 = 14$ ?

$x = 3$

$x = 4$

$x = 10$

$x = 5$

Which graph correctly represents the solution set $x > -2$ ?

Closed circle at $-2$ , arrow pointing right

Open circle at $-2$ , arrow pointing left

Open circle at $-2$ , arrow pointing right

Closed circle at $-2$ , arrow pointing left

A student solves $3x = 12$ for $x$ by dividing both sides by 3. If instead the equation is $ax = 12$ (where $a \neq 0$ ), which expression gives $x$ ?

$x = 12 - a$

$x = 12a$

$x = a + 12$

$x = \frac{12}{a}$

Fluency Practice

Solve each equation or inequality. Show your steps.

Solve for $x$ : $\quad 3(x - 4) = 2x + 1$

Solve for $x$ : $\quad 5x - 3 = 2(x + 6)$

Solve the inequality: $\quad -4x > 20$

$x > -5$

$x < -5$

$x > 5$

$x < 5$

Solve the inequality: $\quad 5 - 2x \leq 11$

Express your answer in inequality notation. Type your answer as "x >= -3" (for example).

The formula for the perimeter of a rectangle is $P = 2l + 2w$ . Which expression correctly gives $l$ in terms of $P$ and $w$ ?

$l = P - 2w$

$l = \frac{P}{2} - w$

$l = \frac{P - w}{2}$

$l = 2P - 2w$

What is the solution set of the equation $4(x + 3) = 4x + 10$ ?

$x = 10$

$x = -2$

All real numbers

No solution

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