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?
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
Combine ax - 7 to get -7x
Combine ax - 7 to get -7x
divide ax by a and 26 by a
divide ax by a and 26 by a
The best first step to solve the equation would be to add 7 to both sides of the equation.
5x−12−6x=−10x+7−1
step by step
First, let's simplify both sides of the equation by combining like terms:
5x - 12 - 6x = -10x + 7 - 1
Combine the x terms on the left side: (5x - 6x = -x)
-x - 12 = -10x + 7 - 1
Combine the constants on the right side: (7 - 1 = 6)
-x - 12 = -10x + 6
Next, let's isolate the variables on one side of the equation. In this case, let's isolate the -x term on the left side by adding 10x to both sides:
-x + 10x - 12 = -10x + 10x + 6
Combine the x terms on the left side: (-x + 10x = 9x)
9x - 12 = 6
Now, let's isolate the constant term on the right side by adding 12 to both sides:
9x - 12 + 12 = 6 + 12
Combine the constants on the left side: (-12 + 12 = 0)
9x = 18
Finally, let's solve for x by dividing both sides of the equation by 9:
9x/9 = 18/9
x = 2
Therefore, the solution to the equation is x = 2.
The number of x's on both sides of the equation is different a≠b
I apologize for the confusion in my previous response. If the number of x's on both sides of the equation is different (a ≠ b), we need to adjust our steps. Here's the correct step-by-step solution:
5x - 12 - 6x = -10x + 7 - 1
Combine the x terms on the left side: (5x - 6x = -x)
-x - 12 = -10x + 6
Now, let's isolate the x terms on one side of the equation. In this case, let's isolate the -x term on the left side by adding 10x to both sides:
-x + 10x - 12 = -10x + 10x + 6
Combine the x terms on the left side: (-x + 10x = 9x)
9x - 12 = 6
Next, let's isolate the constant term on the left side by adding 12 to both sides:
9x - 12 + 12 = 6 + 12
Combine the constants on the left side: (-12 + 12 = 0)
9x = 18
Finally, let's solve for x by dividing both sides of the equation by 9:
9x/9 = 18/9
x = 2
Therefore, the solution to the equation is x = 2.
ax+c1=bx+c2
The number of x's on both sides of the equation is different a≠b
To solve the equation ax + c1 = bx + c2 when a ≠ b, we need to isolate the x term on one side of the equation. Here's the step-by-step solution:
Step 1: Subtract bx from both sides of the equation to isolate the x term on the left side:
ax + c1 - bx = bx + c2 - bx
This simplifies to:
ax - bx + c1 = c2
Step 2: Factor out x from the terms on the left side:
x(a - b) + c1 = c2
Step 3: Divide both sides of the equation by (a - b) to solve for x:
x = (c2 - c1)/(a - b)
Therefore, the solution to the equation ax + c1 = bx + c2 when a ≠ b is x = (c2 - c1)/(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
If the number of x's is the same on both sides of the equation (a = b) but the constants are different (c1 ≠ c2), we can solve the equation by isolating the x term. Here's the step-by-step solution:
Step 1: Subtract c1 from both sides of the equation to isolate the x term on the left side:
ax + c1 - c1 = bx + c2 - c1
Simplifying the equation, we get:
ax = bx + (c2 - c1)
Step 2: Subtract bx from both sides of the equation to gather the x term on the left side:
ax - bx = (c2 - c1)
Factoring out x on the left side, we have:
x(a - b) = (c2 - c1)
Step 3: Divide both sides of the equation by (a - b) to solve for x:
x = (c2 - c1)/(a - b)
Therefore, the solution to the equation ax + c1 = bx + c2 when a = b and c1 ≠ c2 is x = (c2 - c1)/(a - b).
Match the description of the one variable equation with the number of solutions it will have.
ax+c1=bx+c2(3 points)
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
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) - 1 solution
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) - infinitely many solutions
Order the steps for solving the equation: 2x−5=3(4x+5)
(8 points)
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: Distributive Property to get rid of the parentheses on the right side:
2x - 5 = 3 * 4x + 3 * 5
Step 2: Simplify both sides using the Distributive Property:
2x - 5 = 12x + 15
Step 3: Collect the x terms on one side by subtracting 12x from both sides:
2x - 12x - 5 = 12x - 12x + 15
Step 4: Combine like terms on both sides:
-10x - 5 = 15
Order the steps for solving the equation: 2x−5=3(4x+5)
Step 1: Distribute the 3 on the right side:
2x - 5 = 3 * 4x + 3 * 5
Step 2: Simplify the expression on the right side:
2x - 5 = 12x + 15
Step 3: Move all the x terms to one side by subtracting 12x from both sides:
2x - 12x - 5 = 12x - 12x + 15
Step 4: Combine like terms on both sides:
-10x - 5 = 15
x-6 < x/4
To solve the inequality x - 6 < x/4, follow these steps:
Step 1: Get rid of fractions by multiplying both sides of the inequality by 4:
4(x - 6) < 4(x/4)
Simplifying, we have:
4x - 24 < x
Step 2: Move all x terms to one side by subtracting x from both sides:
4x - x - 24 < x - x
Simplifying, we get:
3x - 24 < 0
Step 3: Move the constant term to the other side by adding 24 to both sides:
3x - 24 + 24 < 0 + 24
Simplifying, we have:
3x < 24
Step 4: Divide both sides by 3 to solve for x:
(3x)/3 < 24/3
Simplifying, we get:
x < 8
Therefore, the solution to the inequality x - 6 < x/4 is x < 8.