The number of x's on both sides of the equation is different a≠b - 1 solution
The number of x's is the same on both sides of the equation, and the constant is different a=b, c1≠c2 - infinitely many solutions
The number of x's is the same on both sides of the equation and the constant is also the same a=b, c1=c2 - 1 solution
Match the description of the one variable equation with the number of solutions it will have.
ax+c1=bx+c2
(3 points)
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The number of x's on both sides of the equation is different a≠b
The number of x's is the same on both sides of the equation, and the constant is different a=b, c1≠c2
The number of x's is the same on both sides of the equation and the constant is also the same a=b, c1=c2
5 answers
2x−5=3(4x+5)
Step 1:
Property to get
Step 2:
Property to get
Step 3:
Property to get
Step 4:
Property to get
Step 1:
Property to get
Step 2:
Property to get
Step 3:
Property to get
Step 4:
Property to get
Step 1: Distributive Property to get rid of the parentheses
2x - 5 = 12x + 15
Step 2: Combine like terms by subtracting 12x from both sides
-10x - 5 = 15
Step 3: Add 5 to both sides to isolate the variable
-10x = 20
Step 4: Divide both sides by -10 to solve for x
x = -2
2x - 5 = 12x + 15
Step 2: Combine like terms by subtracting 12x from both sides
-10x - 5 = 15
Step 3: Add 5 to both sides to isolate the variable
-10x = 20
Step 4: Divide both sides by -10 to solve for x
x = -2
Solving the inequality for x, which statement shows a good first step and which is the correct solution?
x−6<x4
(2 points)
Responses
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
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 x to simplify: 1−6x<4
x<6
Divide both sides of the inequality by x to simplify: 1−6x<4
x<6
Multiply both sides by x to get the "x" terms on the same side of the inequality: x−6<4
x−6<x4
(2 points)
Responses
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
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 x to simplify: 1−6x<4
x<6
Divide both sides of the inequality by x to simplify: 1−6x<4
x<6
Multiply both sides by x to get the "x" terms on the same side of the inequality: x−6<4
Divide both sides of the inequality by 4 to simplify: x/4 - 3/2 < x
This is the correct first step.
The correct solution is: x < 12/5 or x < 2.4
This is the correct first step.
The correct solution is: x < 12/5 or x < 2.4
3 answers