Question

solving two - step equations
directions: solve each equation. show your work.

1. 4x - 9 = 19
2. -4x + 6 = 14
3. $\frac{x}{-3}-5 = 4$
4. -5x - 2 = 13
5. -3(x + 1) = 24
6. -5 = 2x - 9
7. $\frac{x}{3}+2.5 = 6.5$
8. $\frac{x}{7}-6 = -3$

Explanation:

1. For the equation \(4x - 9=19\):

• Step1: Isolate the term with \(x\)
• Add 9 to both sides of the equation. \(4x-9 + 9=19 + 9\), which simplifies to \(4x=28\).
• Step2: Solve for \(x\)
• Divide both sides by 4. \(\frac{4x}{4}=\frac{28}{4}\), so \(x = 7\).

1. For the equation \(-4x + 6=14\):

• Step1: Isolate the term with \(x\)
• Subtract 6 from both sides. \(-4x+6 - 6=14 - 6\), which gives \(-4x = 8\).
• Step2: Solve for \(x\)
• Divide both sides by - 4. \(\frac{-4x}{-4}=\frac{8}{-4}\), so \(x=-2\).

1. For the equation \(\frac{x}{-3}-5 = 4\):

• Step1: Isolate the term with \(x\)
• Add 5 to both sides. \(\frac{x}{-3}-5 + 5=4 + 5\), resulting in \(\frac{x}{-3}=9\).
• Step2: Solve for \(x\)
• Multiply both sides by - 3. \(\frac{x}{-3}\times(-3)=9\times(-3)\), so \(x=-27\).

1. For the equation \(-5x-2 = 13\):

• Step1: Isolate the term with \(x\)
• Add 2 to both sides. \(-5x-2 + 2=13 + 2\), getting \(-5x = 15\).
• Step2: Solve for \(x\)
• Divide both sides by - 5. \(\frac{-5x}{-5}=\frac{15}{-5}\), so \(x=-3\).

1. For the equation \(-3(x + 1)=24\):

• Step1: Distribute and simplify
• First, distribute - 3: \(-3x-3 = 24\). Then add 3 to both sides. \(-3x-3 + 3=24 + 3\), giving \(-3x=27\).
• Step2: Solve for \(x\)
• Divide both sides by - 3. \(\frac{-3x}{-3}=\frac{27}{-3}\), so \(x=-9\).

1. For the equation \(-5 = 2x-9\):

• Step1: Isolate the term with \(x\)
• Add 9 to both sides. \(-5 + 9=2x-9 + 9\), resulting in \(4 = 2x\).
• Step2: Solve for \(x\)
• Divide both sides by 2. \(\frac{4}{2}=\frac{2x}{2}\), so \(x = 2\).

1. For the equation \(\frac{x}{3}+2.5 = 6.5\):

• Step1: Isolate the term with \(x\)
• Subtract 2.5 from both sides. \(\frac{x}{3}+2.5-2.5=6.5 - 2.5\), getting \(\frac{x}{3}=4\).
• Step2: Solve for \(x\)
• Multiply both sides by 3. \(\frac{x}{3}\times3=4\times3\), so \(x = 12\).

1. For the equation \(\frac{x}{7}-6=-3\):

• Step1: Isolate the term with \(x\)
• Add 6 to both sides. \(\frac{x}{7}-6 + 6=-3 + 6\), resulting in \(\frac{x}{7}=3\).
• Step2: Solve for \(x\)
• Multiply both sides by 7. \(\frac{x}{7}\times7=3\times7\), so \(x = 21\).

Answer:

1. \(x = 7\)
2. \(x=-2\)
3. \(x=-27\)
4. \(x=-3\)
5. \(x=-9\)
6. \(x = 2\)
7. \(x = 12\)
8. \(x = 21\)