Back to Exercise: Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions

Classifying Linear Equations by Their Number of Solutions

Work through each section in order. Solve each equation completely, then state whether it has one solution, infinitely many solutions, or no solution. Show your work where indicated.

Grade 8·20 problems·~28 min·Common Core Math - Grade 8·standard·8-ee-c-7a

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Recall / Warm-Up

Solve for $x$ : $3x + 4 = 19$ .

$x = 5$

$x = 7$

$x = \frac{19}{3}$

$x = 15$

Solve for $x$ : $5x - 2 = 3x + 8$ .

A value is a solution to an equation when it makes the equation true after you substitute it in. The statement $7 = 7$ has no variable in it. Is $7 = 7$ true or false?

True — both sides are the same number.

False — there is no variable, so it cannot be true.

It depends on the value of $x$ .

Fluency Practice

Solve $4x - 5 = 2x + 9$ . Enter the value of $x$ .

Solve $6(x - 2) = 4x + 2$ . Enter the value of $x$ .

Solve $3(x - 1) + 3 = 3x$ . How many solutions does the equation have?

One solution: $x = 0$

No solution

Infinitely many solutions

One solution: $x = 3$

Solve $5(x + 2) = 5x - 1$ . What is the terminal form, and how many solutions are there?

$10 = -1$ ; no solution

$x = -1$ ; one solution

$0 = 0$ ; infinitely many solutions

$x = 11$ ; one solution

Three equations are shown. Which one has exactly one solution?

$3x + 5 = 3x + 11$

$3x + 5 = 3x + 5$

$3x + 5 = x + 11$

$2(x + 4) = 2x + 8$

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