This is a sample of a curriculum practice pack. Add your email to unlock one like this for every topic, K–12 — free.

Algebra 1 Essentials

Sample curriculum practice pack · every problem verified · Best Math Resources

1.Linear equations
Solve for $x$ : $4x + 7 = 23$ .
2.Linear equations
Solve for $x$ : $5x - 7 = 18$ .
3.Linear equations
Solve for $x$ : $3(x+4) - 5 = 2x + 9$
4.Linear equations
Solve for $x$ : $3x + 7 = 22$
5.Linear equations
Solve for $x$ : $3x + 5 = 20$
6.Factoring quadratics
Factor completely: $6x^2 + 7x - 20$ .
7.Factoring quadratics
Factor the quadratic expression completely: $3x^2 + 11x + 6$ .
8.Factoring quadratics
Factor the quadratic expression completely: $2x^2 + 7x - 15$ .
9.Factoring quadratics
Factor the quadratic expression completely: $2x^2 + 7x + 3$ .

Answer key

Algebra 1 Essentials · worked solutions

1.Linear equations
Solve for $x$ : $4x + 7 = 23$ .
1. Start with $4x + 7 = 23$ .
2. Subtract $7$ from both sides: $4x = 16$ .
3. Divide both sides by $4$ : $x = 4$ .
Answer:
$x = 4$
2.Linear equations
Solve for $x$ : $5x - 7 = 18$ .
1. Start with $5x - 7 = 18$ .
2. Add $7$ to both sides: $5x = 25$ .
3. Divide both sides by $5$ : $x = 5$ .
Answer:
$x = 5$
3.Linear equations
Solve for $x$ : $3(x+4) - 5 = 2x + 9$
1. Distribute the 3 on the left side: $3x + 12 - 5 = 2x + 9$
2. Combine like terms on the left side: $3x + 7 = 2x + 9$
3. Subtract $2x$ from both sides: $x + 7 = 9$
4. Subtract 7 from both sides: $x = 2$
Answer:
$x = 2$
4.Linear equations
Solve for $x$ : $3x + 7 = 22$
1. Start with the equation $3x + 7 = 22$ .
2. Subtract 7 from both sides: $3x = 22 - 7 = 15$ .
3. Divide both sides by 3: $x = \frac{15}{3} = 5$ .
Answer:
$x = 5$
5.Linear equations
Solve for $x$ : $3x + 5 = 20$
1. Start with the equation: $3x + 5 = 20$
2. Subtract 5 from both sides: $3x = 15$
3. Divide both sides by 3: $x = 5$
Answer:
$x = 5$
6.Factoring quadratics
Factor completely: $6x^2 + 7x - 20$ .
1. We need two numbers that multiply to $6 \cdot (-20) = -120$ and add to $7$ .
2. The numbers $15$ and $-8$ work since $15 \cdot (-8) = -120$ and $15 + (-8) = 7$ .
3. Rewrite the middle term: $6x^2 + 15x - 8x - 20$ .
4. Group: $(6x^2 + 15x) + (-8x - 20)$ .
5. Factor each group: $3x(2x + 5) - 4(2x + 5)$ .
6. Factor out the common binomial: $(2x + 5)(3x - 4)$ .
Answer:
$(2x + 5)(3x - 4)$
7.Factoring quadratics
Factor the quadratic expression completely: $3x^2 + 11x + 6$ .
1. We need to factor $3x^2 + 11x + 6$ where the leading coefficient is 3.
2. Multiply the leading coefficient and the constant term: $3 \times 6 = 18$ .
3. Find two numbers that multiply to $18$ and add to $11$ : these numbers are $9$ and $2$ .
4. Rewrite the middle term using these numbers: $3x^2 + 9x + 2x + 6$ .
5. Group the terms: $(3x^2 + 9x) + (2x + 6)$ .
6. Factor out the greatest common factor from each group: $3x(x+3) + 2(x+3)$ .
7. Factor out the common binomial factor $(x+3)$ : $(3x+2)(x+3)$ .
8. Check by expanding: $(3x+2)(x+3) = 3x^2 + 9x + 2x + 6 = 3x^2 + 11x + 6$ , which matches the original expression.
Answer:
$(3x+2)(x+3)$
8.Factoring quadratics
Factor the quadratic expression completely: $2x^2 + 7x - 15$ .
1. We need two numbers that multiply to $2 \times (-15) = -30$ and add to $7$ .
2. These numbers are $10$ and $-3$ , since $10 \times (-3) = -30$ and $10 + (-3) = 7$ .
3. Rewrite the middle term: $2x^2 + 10x - 3x - 15$ .
4. Group terms: $(2x^2 + 10x) + (-3x - 15)$ .
5. Factor each group: $2x(x+5) - 3(x+5)$ .
6. Factor out the common binomial $(x+5)$ : $(2x-3)(x+5)$ .
Answer:
$(2x-3)(x+5)$
9.Factoring quadratics
Factor the quadratic expression completely: $2x^2 + 7x + 3$ .
1. We want to factor $2x^2 + 7x + 3$ where $a=2$ , $b=7$ , $c=3$ .
2. Multiply $a \cdot c = 2 \cdot 3 = 6$ .
3. Find two numbers that multiply to $6$ and add to $7$ : these are $6$ and $1$ .
4. Rewrite the middle term using these numbers: $2x^2 + 6x + x + 3$ .
5. Group the terms: $(2x^2 + 6x) + (x + 3)$ .
6. Factor out the common factor from each group: $2x(x+3) + 1(x+3)$ .
7. Factor out the common binomial factor: $(2x+1)(x+3)$ .
Answer:
$(2x+1)(x+3)$