Section 4.3 - Equation Solving Strategies

Explanation
The equation -2x + 6 = 4x can be solved by first combining like terms, which gives 6 = 6x. Then, dividing both sides of the equation by 6 gives x = 1.

Explanation
By subtracting -3x from both sides of the equation, we get -5x + 3x + 1 = -7. Simplifying further, we have -2x + 1 = -7. By subtracting 1 from both sides, we get -2x = -8. Dividing both sides by -2, we find that x = 4.

Explanation
The equation 5(x - 2) = 35 can be solved by first distributing the 5 to both terms inside the parentheses, giving us 5x - 10 = 35. Then, we can add 10 to both sides to isolate the variable, resulting in 5x = 45. Finally, dividing both sides by 5 gives us x = 9.

Explanation
To solve the equation x/6 + 2 = 5, we first subtract 2 from both sides to isolate the term x/6. This gives us x/6 = 3. To solve for x, we multiply both sides by 6 to get rid of the fraction. This gives us x = 18. Therefore, the correct answer is x = 18.

Explanation
When Jon mows a lawn in 2 hours, this means that he can complete 1/2 of the lawn in 1 hour. Similarly, Baxter can complete 1/3 of the lawn in 1 hour. When they work together, their combined work rate is the sum of their individual work rates. Therefore, they can complete 1/2 + 1/3 = 5/6 of the lawn in 1 hour. To find out how long it will take them to complete the entire lawn, we can take the reciprocal of 5/6, which is 6/5. So, it will take them 6/5 hours to complete the lawn when working together.

Explanation
Jane and Dave are running towards each other, so their combined speed is 10 km/h + 15 km/h = 25 km/h. They need to cover a distance of 15 km to meet. The time it takes to cover a distance is equal to distance divided by speed. Therefore, the time it takes for them to meet is 15 km / 25 km/h = 3/5 h.

Explanation
The equation 3x + 4 = 3x + 4 is an identity, meaning that it is true for all values of x. This is because the equation is symmetrical, with the same terms on both sides, and no variable that can be canceled out or simplified. Therefore, any value of x will satisfy the equation, resulting in infinitely many solutions.

Explanation
To solve the equation, Leo should first multiply all terms by the least common denominator (LCD). This step is necessary because it eliminates the fractions in the equation and makes it easier to solve. By multiplying both sides of the equation by the LCD, Leo will be able to simplify the equation and continue solving it to find the value of x.

Explanation
To solve the equation, we can start by multiplying both sides of the equation by 15 to eliminate the fractions. This gives us 3a + 30 = 5a. Then, we can subtract 3a from both sides to get 30 = 2a. Finally, dividing both sides by 2 gives us a = 15.

Explanation
The correct answer is 24/7 hours. When two pipes are working together, their combined rate of draining the pool is the sum of their individual rates. The first pipe can drain the pool in 6 hours, which means it can drain 1/6th of the pool in 1 hour. Similarly, the second pipe can drain the pool in 8 hours, so it can drain 1/8th of the pool in 1 hour. When both pipes are working together, they can drain 1/6th + 1/8th = 7/24th of the pool in 1 hour. Therefore, it will take them 24/7 hours to drain the entire pool.