Math Core

This test covers equations with variables on both sides, equations with the distributive property, and deciding how many solutions a linear equation has.

Question 1

Solve $8x - 5 = 3x + 20$ for $x$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 2

Solve $2y + 17 = 7y - 13$ for $y$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 3

Solve $1.2n + 3 = 0.4n + 9.4$ for $n$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 4

Taxi A charges $4 plus $2.50 per mile. Taxi B charges $7 plus $1.75 per mile. For how many miles do the two taxis cost the same?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 5

Which equation has the solution $x = 2$ ?

Question 6

Solve $5(x - 2) = 35$ for $x$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 7

Solve $-4(3 - 2a) = 2a + 12$ for $a$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 8

Solve $3(2k + 5) - 2(k - 1) = 41$ for $k$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 9

A student solved $9 - 2(x + 1) = 3$ . The first line of the work was $9 - 2x + 2 = 3$ . What was the mistake?

Question 10

Solve $\dfrac{2}{3}(9x - 6) = 4x + 2$ for $x$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 11

Twice the sum of a number and $7$ equals $4$ less than $5$ times the number. Find the number.

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 12

How many solutions does $3(x + 4) = 3x + 12$ have?

Question 13

How many solutions does $2(x - 3) + 5 = 2x + 1$ have?

Question 14

How many solutions does $4x - 7 = 4(x - 1) - 3 + x$ have?

Question 15

What value of $a$ makes $ax + 9 = 3(2x + 3)$ have infinitely many solutions?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.