College

Create and solve a linear equation that represents the model, where circles and a square are shown evenly balanced on a balance beam.

A. [tex]x = 5 + 7 ; x = 12[/tex]
B. [tex]x + 7 = 5 ; x = -2[/tex]
C. [tex]x + 5 = 7 ; x = 2[/tex]
D. [tex]x + 7 = 12 ; x = 5[/tex]

Answer :

Sure! Let's go through each equation step-by-step and solve them to find the correct values of [tex]\( x \)[/tex].

1. Equation: [tex]\( x = 5 + 7 \)[/tex]
- Here, you just need to add 5 and 7.
- [tex]\( x = 5 + 7 \)[/tex]
- [tex]\( x = 12 \)[/tex]

2. Equation: [tex]\( x + 7 = 5 \)[/tex]
- To isolate [tex]\( x \)[/tex], subtract 7 from both sides.
- [tex]\( x + 7 - 7 = 5 - 7 \)[/tex]
- [tex]\( x = -2 \)[/tex]

3. Equation: [tex]\( x + 5 = 7 \)[/tex]
- To isolate [tex]\( x \)[/tex], subtract 5 from both sides.
- [tex]\( x + 5 - 5 = 7 - 5 \)[/tex]
- [tex]\( x = 2 \)[/tex]

4. Equation: [tex]\( x + 7 = 12 \)[/tex]
- To isolate [tex]\( x \)[/tex], subtract 7 from both sides.
- [tex]\( x + 7 - 7 = 12 - 7 \)[/tex]
- [tex]\( x = 5 \)[/tex]

Based on these calculations, the solutions for each of the equations are:
1. [tex]\( x = 12 \)[/tex]
2. [tex]\( x = -2 \)[/tex]
3. [tex]\( x = 2 \)[/tex]
4. [tex]\( x = 5 \)[/tex]

Thus, the correct steps and solutions are provided for the given equations.

Other Questions