Question

i 15b
(9) $3x - (x - 2) = 8$
$3x - x + 2 = 8$
$2x = 6$
$x = 3$
(10) $4 - (2x + 3) = 4x$
$4 - 2x - 3 = 4x$
$-6x = -1$
$x = 6$
(11) $3x + 2(x - 4) = 7$
$3x + 2x - 8 = 7$
$5x = 15$
$x = 3$
(12) $5 - 3(x - 2) = -x + 5$
$5 - 3x + 6 = -x + 5$
$-2x = -6$
$x = 3$
(13) $3x - (4 - 2x) = x + 8$
$3x - 4 + 2x = x + 8$
$4x = 12$
$x = 3$
(14) $15 - 2(x + 3) = x + 9$
$15 - 2x - 6 = x + 9$
$-3x = 0$
$x = 0$
(15) $5 - 4(x - 3) = x - 2(x - 1)$
$5 - 4x + 12 = x - 2x + 1$
$-x = -16$
$x = 16$
(16) $x - 2(x + 2) = 5(x - 1) + 3$

Explanation:

Let's solve equation (10) step by step as an example (since there are multiple equations, we can pick one to demonstrate). The equation is \(4 - (2x + 3) = 4x\).

Step 1: Simplify the left - hand side

First, we use the distributive property \(a-(b + c)=a - b - c\). For \(4-(2x + 3)\), we have \(4-2x - 3\). Then, simplify \(4-3\) to get \(1-2x\). So the equation becomes \(1-2x = 4x\).

Step 2: Move the terms with \(x\) to one side

Add \(2x\) to both sides of the equation. According to the addition property of equality, if \(a=b\), then \(a + c=b + c\). So \(1-2x+2x=4x + 2x\), which simplifies to \(1 = 6x\).

Step 3: Solve for \(x\)

Divide both sides of the equation by 6. According to the division property of equality, if \(a=b\), then \(\frac{a}{c}=\frac{b}{c}(c
eq0)\). So \(\frac{1}{6}=\frac{6x}{6}\), which gives \(x=\frac{1}{6}\) (Note: The original hand - written answer in the picture seems to be wrong. We solve it correctly here).

If we want to solve equation (9): \(3x-(x - 2)=8\)

Step 1: Simplify the left - hand side

Use the distributive property \(a-(b - c)=a - b + c\). For \(3x-(x - 2)\), we get \(3x-x + 2\). Combine like terms \(3x-x\) to get \(2x+2\). The equation becomes \(2x + 2=8\).

Step 2: Isolate the term with \(x\)

Subtract 2 from both sides of the equation. By the subtraction property of equality, \(2x+2 - 2=8 - 2\), which simplifies to \(2x=6\).

Step 3: Solve for \(x\)

Divide both sides by 2. Using the division property of equality, \(\frac{2x}{2}=\frac{6}{2}\), so \(x = 3\) (this matches the hand - written answer in the picture).

If you want to solve a specific equation from the list (such as (11), (12), etc.), you can follow a similar process of simplifying the left - hand side (and right - hand side if necessary), combining like terms, and then using the properties of equality to solve for \(x\).

Answer:

Step 1: Simplify the left - hand side

Use the distributive property \(a-(b - c)=a - b + c\). For \(3x-(x - 2)\), we get \(3x-x + 2\). Combine like terms \(3x-x\) to get \(2x+2\). The equation becomes \(2x + 2=8\).

Step 2: Isolate the term with \(x\)

Subtract 2 from both sides of the equation. By the subtraction property of equality, \(2x+2 - 2=8 - 2\), which simplifies to \(2x=6\).

Step 3: Solve for \(x\)

Divide both sides by 2. Using the division property of equality, \(\frac{2x}{2}=\frac{6}{2}\), so \(x = 3\) (this matches the hand - written answer in the picture).

If you want to solve a specific equation from the list (such as (11), (12), etc.), you can follow a similar process of simplifying the left - hand side (and right - hand side if necessary), combining like terms, and then using the properties of equality to solve for \(x\).