Question

1. 2x + 5x - 7 - 2x = 12 - 4 = 16
2. 5x - 7 = 2x
3. the average number of points a basketball team scored for three games was 63 points. in the first two games, they scored the same number of points, which was 6 points more than they scored in the third game. write and solve an equation to find the number of points the team scored in each game.

Explanation:

Step1: Set up the equation for the average

Let the number of points scored in the first - two games be \(x\) each. The number of points scored in the third game is \(x + 6\). The average of the three - game scores is \(\frac{x + x+(x + 6)}{3}\), and we know the average number of points is \(\frac{\text{total points}}{\text{number of games}}\), and the total points for the three games is 63. So the equation is \(\frac{x+x+(x + 6)}{3}=63\).

Step2: Simplify the left - hand side of the equation

Combine like terms in the numerator: \(\frac{3x + 6}{3}\). Using the distributive property of division over addition \(\frac{3x+6}{3}=\frac{3x}{3}+\frac{6}{3}=x + 2\). So our equation becomes \(x + 2=63\).

Step3: Solve for \(x\)

Subtract 2 from both sides of the equation: \(x=63 - 2=61\).

Step4: Find the score in each game

The score in the first two games is \(x = 61\) points each. The score in the third game is \(x + 6=61+6 = 67\) points.

Answer:

The team scored 61 points in each of the first two games and 67 points in the third game.