Question

solve each equation for x. assume a ≠ 0.

1. ax + 3 = 23
2. 4 = ax - 14
3. ax - 5 = 19
4. 6 + ax = -29
5. $\frac{8}{ax}$ - 5 = -3
6. 18 - ax = 42
7. 5 = $\frac{5}{ax}$ + 1
8. -3 = ax + 11
9. -7 = -ax - 16

Explanation:

1. For equation \(ax + 3=23\) (Question 18):

• Step 1: Isolate the term with \(x\)
• Subtract 3 from both sides of the equation: \(ax+3 - 3=23 - 3\), which simplifies to \(ax = 20\).
• Step 2: Solve for \(x\)
• Since \(a

eq0\), divide both sides by \(a\): \(x=\frac{20}{a}\).

1. For equation \(4 = ax-14\) (Question 19):

• Step 1: Isolate the term with \(x\)
• Add 14 to both sides of the equation: \(4 + 14=ax-14 + 14\), which simplifies to \(ax=18\).
• Step 2: Solve for \(x\)
• Since \(a

eq0\), divide both sides by \(a\): \(x = \frac{18}{a}\).

1. For equation \(ax-5 = 19\) (Question 20):

• Step 1: Isolate the term with \(x\)
• Add 5 to both sides of the equation: \(ax-5 + 5=19 + 5\), which simplifies to \(ax = 24\).
• Step 2: Solve for \(x\)
• Since \(a

eq0\), divide both sides by \(a\): \(x=\frac{24}{a}\).

1. For equation \(6+ax=-29\) (Question 21):

• Step 1: Isolate the term with \(x\)
• Subtract 6 from both sides of the equation: \(6+ax - 6=-29 - 6\), which simplifies to \(ax=-35\).
• Step 2: Solve for \(x\)
• Since \(a

eq0\), divide both sides by \(a\): \(x =-\frac{35}{a}\).

1. For equation \(\frac{8}{ax}-5=-3\) (Question 22):

• Step 1: Isolate the fraction with \(x\)
• Add 5 to both sides of the equation: \(\frac{8}{ax}-5 + 5=-3 + 5\), which simplifies to \(\frac{8}{ax}=2\).
• Step 2: Cross - multiply
• We get \(2ax = 8\).
• Step 3: Solve for \(x\)
• Divide both sides by \(2a\) (since \(a

eq0\)): \(x=\frac{4}{a}\).

1. For equation \(18-ax = 42\) (Question 23):

• Step 1: Isolate the term with \(x\)
• Subtract 18 from both sides: \(18-ax - 18=42 - 18\), which simplifies to \(-ax = 24\).
• Step 2: Solve for \(x\)
• Divide both sides by \(-a\) (since \(a

eq0\)): \(x=-\frac{24}{a}\).

1. For equation \(5=\frac{5}{ax}+1\) (Question 24):

• Step 1: Isolate the fraction with \(x\)
• Subtract 1 from both sides: \(5 - 1=\frac{5}{ax}+1 - 1\), which simplifies to \(\frac{5}{ax}=4\).
• Step 2: Cross - multiply
• We get \(4ax = 5\).
• Step 3: Solve for \(x\)
• Divide both sides by \(4a\) (since \(a

eq0\)): \(x=\frac{5}{4a}\).

1. For equation \(-3=ax + 11\) (Question 25):

• Step 1: Isolate the term with \(x\)
• Subtract 11 from both sides: \(-3-11=ax + 11-11\), which simplifies to \(ax=-14\).
• Step 2: Solve for \(x\)
• Divide both sides by \(a\) (since \(a

eq0\)): \(x=-\frac{14}{a}\).

1. For equation \(-7=-ax-16\) (Question 26):

• Step 1: Isolate the term with \(x\)
• Add 16 to both sides: \(-7 + 16=-ax-16 + 16\), which simplifies to \(9=-ax\).
• Step 2: Solve for \(x\)
• Divide both sides by \(-a\) (since \(a

eq0\)): \(x=-\frac{9}{a}\).

Answer:

1. \(x=\frac{20}{a}\)
2. \(x=\frac{18}{a}\)
3. \(x=\frac{24}{a}\)
4. \(x =-\frac{35}{a}\)
5. \(x=\frac{4}{a}\)
6. \(x=-\frac{24}{a}\)
7. \(x=\frac{5}{4a}\)
8. \(x=-\frac{14}{a}\)
9. \(x=-\frac{9}{a}\)