Let's solve each of these equations step by step:

Problem 7:

$4(3x - 10) + 7 = 15$ Step 1: Expand the equation. $4(3x - 10) = 12x - 40$ So the equation becomes: $12x - 40 + 7 = 15$

Step 2: Combine like terms. $12x - 33 = 15$

Step 3: Add 33 to both sides. $12x = 48$

Step 4: Divide both sides by 12. $x = 4$

Problem 8:

$6 - 5(2x + 1) = 21$ Step 1: Expand the equation. $6 - 5(2x + 1) = 6 - 10x - 5$ Simplify it: $1 - 10x = 21$

Step 2: Subtract 1 from both sides. $-10x = 20$

Step 3: Divide both sides by -10. $x = -2$

Problem 9:

$2 - \frac{3}{4}(8x - 6) = 11$ Step 1: Distribute $\frac{3}{4}$ across the terms inside the parentheses. $\frac{3}{4}(8x - 6) = \frac{3}{4} \times 8x - \frac{3}{4} \times 6 = 6x - 4.5$ So the equation becomes: $2 - (6x - 4.5) = 11$ This simplifies to: $2 - 6x + 4.5 = 11$

Step 2: Combine like terms. $6.5 - 6x = 11$

Step 3: Subtract 6.5 from both sides. $-6x = 4.5$

Step 4: Divide both sides by -6. $x = -\frac{3}{4} \quad \text{or} \quad x = -0.75$

Problem 10:

$0.2(4 - 5x) + 1 = 2.4$ Step 1: Expand the equation. $0.2(4 - 5x) = 0.8 - x$ So the equation becomes: $0.8 - x + 1 = 2.4$

Step 2: Combine like terms. $1.8 - x = 2.4$

Step 3: Subtract 1.8 from both sides. $-x = 0.6$

Step 4: Multiply both sides by -1. $x = -0.6$

If you'd like any further details or have questions about specific steps, feel free to ask!

Related Questions:

1. How do you distribute terms across parentheses in equations?
2. How do you handle fractions in equations, like in problem 9?
3. What are the steps for isolating the variable $x$ in an equation?
4. How can you check if your solution for $x$ is correct?
5. What are like terms, and why do we combine them in equations?

Tip:

Always simplify your equation by combining like terms and eliminating fractions or decimals early in the process.