Answer :
Of course! Let's match each equation with its solution step-by-step:
### Equation 1: [tex]\( x - 6 = -4 \)[/tex]
To solve for [tex]\( x \)[/tex]:
1. Isolate [tex]\( x \)[/tex] by adding 6 to both sides of the equation:
[tex]\[ x - 6 + 6 = -4 + 6 \][/tex]
2. Simplify:
[tex]\[ x = 2 \][/tex]
So, the solution for [tex]\( x - 6 = -4 \)[/tex] is [tex]\( x = 2 \)[/tex].
### Equation 2: [tex]\( x + 3 = -7 \)[/tex]
To solve for [tex]\( x \)[/tex]:
1. Isolate [tex]\( x \)[/tex] by subtracting 3 from both sides of the equation:
[tex]\[ x + 3 - 3 = -7 - 3 \][/tex]
2. Simplify:
[tex]\[ x = -10 \][/tex]
So, the solution for [tex]\( x + 3 = -7 \)[/tex] is [tex]\( x = -10 \)[/tex].
### Equation 3: [tex]\( 5x = -2 \)[/tex]
To solve for [tex]\( x \)[/tex]:
1. Isolate [tex]\( x \)[/tex] by dividing both sides by 5:
[tex]\[ \frac{5x}{5} = \frac{-2}{5} \][/tex]
2. Simplify:
[tex]\[ x = -0.4 \][/tex]
So, the solution for [tex]\( 5x = -2 \)[/tex] is [tex]\( x = -0.4 \)[/tex].
### Equation 4: [tex]\( 0.5x = 5 \)[/tex]
To solve for [tex]\( x \)[/tex]:
1. Isolate [tex]\( x \)[/tex] by dividing both sides by 0.5:
[tex]\[ \frac{0.5x}{0.5} = \frac{5}{0.5} \][/tex]
2. Simplify:
[tex]\[ x = 10 \][/tex]
So, the solution for [tex]\( 0.5x = 5 \)[/tex] is [tex]\( x = 10 \)[/tex].
### Matching the equations with their solutions:
[tex]\[ \begin{array}{ll} \text { Equation } & \text { Solution } \\ x-6=-4 & x=2 \\ x+3=-7 & x=-10 \\ 5 x=-2 & x=-0.4 \\ 0.5 x=5 & x=10 \\ \end{array} \][/tex]
### Equation 1: [tex]\( x - 6 = -4 \)[/tex]
To solve for [tex]\( x \)[/tex]:
1. Isolate [tex]\( x \)[/tex] by adding 6 to both sides of the equation:
[tex]\[ x - 6 + 6 = -4 + 6 \][/tex]
2. Simplify:
[tex]\[ x = 2 \][/tex]
So, the solution for [tex]\( x - 6 = -4 \)[/tex] is [tex]\( x = 2 \)[/tex].
### Equation 2: [tex]\( x + 3 = -7 \)[/tex]
To solve for [tex]\( x \)[/tex]:
1. Isolate [tex]\( x \)[/tex] by subtracting 3 from both sides of the equation:
[tex]\[ x + 3 - 3 = -7 - 3 \][/tex]
2. Simplify:
[tex]\[ x = -10 \][/tex]
So, the solution for [tex]\( x + 3 = -7 \)[/tex] is [tex]\( x = -10 \)[/tex].
### Equation 3: [tex]\( 5x = -2 \)[/tex]
To solve for [tex]\( x \)[/tex]:
1. Isolate [tex]\( x \)[/tex] by dividing both sides by 5:
[tex]\[ \frac{5x}{5} = \frac{-2}{5} \][/tex]
2. Simplify:
[tex]\[ x = -0.4 \][/tex]
So, the solution for [tex]\( 5x = -2 \)[/tex] is [tex]\( x = -0.4 \)[/tex].
### Equation 4: [tex]\( 0.5x = 5 \)[/tex]
To solve for [tex]\( x \)[/tex]:
1. Isolate [tex]\( x \)[/tex] by dividing both sides by 0.5:
[tex]\[ \frac{0.5x}{0.5} = \frac{5}{0.5} \][/tex]
2. Simplify:
[tex]\[ x = 10 \][/tex]
So, the solution for [tex]\( 0.5x = 5 \)[/tex] is [tex]\( x = 10 \)[/tex].
### Matching the equations with their solutions:
[tex]\[ \begin{array}{ll} \text { Equation } & \text { Solution } \\ x-6=-4 & x=2 \\ x+3=-7 & x=-10 \\ 5 x=-2 & x=-0.4 \\ 0.5 x=5 & x=10 \\ \end{array} \][/tex]
