Sure, let's solve the given equations step-by-step.
Equation (a): [tex]\( 7x - 2 = 12 \)[/tex]
1. Start by isolating [tex]\( x \)[/tex] on one side of the equation. Add 2 to both sides:
[tex]\[
7x - 2 + 2 = 12 + 2
\][/tex]
2. This simplifies to:
[tex]\[
7x = 14
\][/tex]
3. Next, divide both sides by 7 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{14}{7}
\][/tex]
4. Simplifying this division gives:
[tex]\[
x = 2
\][/tex]
Equation (c): [tex]\( 3x - 1 = 2 \)[/tex]
1. Isolate [tex]\( x \)[/tex] by adding 1 to both sides:
[tex]\[
3x - 1 + 1 = 2 + 1
\][/tex]
2. This simplifies to:
[tex]\[
3x = 3
\][/tex]
3. Divide both sides by 3 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{3}{3}
\][/tex]
4. Simplifying this division gives:
[tex]\[
x = 1
\][/tex]
Equation: [tex]\( 5x - 3 = 17 \)[/tex]
1. Start by isolating [tex]\( x \)[/tex]. Add 3 to both sides:
[tex]\[
5x - 3 + 3 = 17 + 3
\][/tex]
2. This simplifies to:
[tex]\[
5x = 20
\][/tex]
3. Divide both sides by 5 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{20}{5}
\][/tex]
4. Simplifying this division gives:
[tex]\[
x = 4
\][/tex]
Equation: [tex]\( 6x - 5 = 25 \)[/tex]
1. Isolate [tex]\( x \)[/tex] by adding 5 to both sides:
[tex]\[
6x - 5 + 5 = 25 + 5
\][/tex]
2. This simplifies to:
[tex]\[
6x = 30
\][/tex]
3. Divide both sides by 6 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{30}{6}
\][/tex]
4. Simplifying this division gives:
[tex]\[
x = 5
\][/tex]
Equation: [tex]\( -7 = 49 \)[/tex]
1. This equation states that [tex]\(-7\)[/tex] is equal to [tex]\(49\)[/tex], which is clearly a contradiction. There is no possible value of [tex]\(x\)[/tex] that can make this equation true, hence it has no solution.
To summarize:
- For [tex]\( 7x - 2 = 12 \)[/tex], the solution is [tex]\( x = 2 \)[/tex].
- For [tex]\( 3x - 1 = 2 \)[/tex], the solution is [tex]\( x = 1 \)[/tex].
- For [tex]\( 5x - 3 = 17 \)[/tex], the solution is [tex]\( x = 4 \)[/tex].
- For [tex]\( 6x - 5 = 25 \)[/tex], the solution is [tex]\( x = 5 \)[/tex].
- The equation [tex]\( -7 = 49 \)[/tex] has no solution.
