Solving the inequality for x, which statement shows a good first step and which is the correct solution?
x−6<x4
(2 points)
Responses
Multiply both sides by 4 to clear the inequality of fractions: 4x−24<x
Multiply both sides by 4 to clear the inequality of fractions: 4x−24<x
Divide both sides of the inequality by 4 to simplify: x4−32<x
Divide both sides of the inequality by 4 to simplify: x4−32<x
Divide both sides of the inequality by x to simplify: 1−6x<4
x<6
The correct first step would be to add 6 to both sides of the inequality: x−6 < x+4.
The correct solution would be: x < 10.
Solving the inequality for x, which statement shows a good first step and which is the correct solution?
x−6<x4
(2 points)
Responses
Multiply both sides by 4 to clear the inequality of fractions: 4x−24<x
Multiply both sides by 4 to clear the inequality of fractions: 4x−24<x
Divide both sides of the inequality by 4 to simplify: x4−32<x
Divide both sides of the inequality by 4 to simplify: x4−32<x
Divide both sides of the inequality by x to simplify: 1−6x<4
x<6
Divide both sides of the inequality by x to simplify: 1−6x<4
x<6
The correct first step would be to add 6 to both sides of the inequality: x−6 < x+4.
The correct solution would be: x < 10.
You need to solve this equation for x: ax−7=26
Which would be the best first step you could make to solve the equation?
(1 point)
Responses
Combine ax - 7 to get -7x
Combine ax - 7 to get -7x
add 7 to both sides of the equation
add 7 to both sides of the equation
subtract 7 from the left side of the equation
subtract 7 from the left side of the equation
The best first step to solve the equation ax - 7 = 26 would be to add 7 to both sides of the equation.
The correct first step is to add 6 to both sides of the inequality: x−6+6<x+4.
This simplifies to: x<-2.
So, the correct solution is x<-2.
The first statement, "Multiply both sides by 4 to clear the inequality of fractions: 4x−24<x," is a good first step in solving the inequality. However, the correct solution is given by the third statement, "Divide both sides of the inequality by 4 to simplify: x/4−8<x."
To solve the inequality x-6 < x/4, we can follow these steps:
Step 1: To get rid of the fractions, multiply both sides of the inequality by the common denominator, which is 4. This results in 4(x-6) < x.
Step 2: Distribute the 4 to both terms inside the parentheses: 4x - 24 < x.
Step 3: Now, we want to isolate x. To do this, we need to move all terms with x to one side of the inequality. In this case, subtract x from both sides: 3x - 24 < 0.
Step 4: Finally, to solve for x, add 24 to both sides: 3x < 24.
Step 5: Divide both sides of the inequality by 3 to simplify and solve for x: x < 8.
Therefore, the correct solution is x < 8.