Question

write the following statements in symbols.

1. 7 more than twice a number is 11.
2. twice the sum of a number and 8 is 40.

simplify.

1. \\(3a + 2a\\)
2. \\(-(4y - 7)\\)
3. \\(11 - 2(x - 5)\\)
4. \\(3(x - 2) - 2(5x - 7y + 1)\\)

section 7-2
solve.

1. \\(x - 5 = 8\\)
2. \\(x - 15 = -7\\)
3. \\(x + 7 = 10\\)
4. \\(3 + y = -5\\)
5. \\(3x + 4 = 19\\)
6. \\(5 = 3x - 7\\)
7. \\(5x - 12 = 9x\\)
8. \\(4x = -28\\)
9. \\(3 = \frac{1}{5}x\\)
10. \\(0.6 = -a\\)
11. \\(42 = -\frac{6}{7}x\\)

Explanation:

Translate statements to symbols

Using the Algebraic Translation knowledge point

$$
LATEXBLOCK0
$$

Simplify algebraic expressions

Using the Combining Like Terms and Distributive Property knowledge points

$$
LATEXBLOCK1
$$

Solve one-step equations

Using the One-Step Equations knowledge point

$$
LATEXBLOCK2
$$

Solve two-step equations

Using the Two-Step Equations knowledge point

$$
LATEXBLOCK3
$$

Solve multi-step linear equations

Using the Linear Equations knowledge point

$$
LATEXBLOCK4
$$

Answer:

Question 15

\(2x + 7 = 11\)

Question 17

\(2(x + 8) = 40\)

Question 19

\(5a\)

Question 22

\(-4y + 7\)

Question 25

\(-2x + 21\)

Question 28

\(-7x + 14y - 8\)

Question 31

\(x = 13\)

Question 34

\(x = 8\)

Question 37

\(x = 3\)

Question 40

\(y = -8\)

Question 43

\(x = 5\)

Question 46

\(x = 4\)

Question 49

\(x = -3\)

Question 52

\(x = -7\)

Question 55

\(x = 15\)

Question 58

\(a = -0.6\)

Question 61

\(y = -\frac{1}{7}\)