A student solves the following equation:
Problem: 2(x−3)+3x=19
Step 1: 2x−6+3x=19
Step 2: (2x+3x)−6=19
Step 3: 5x−6=19
Step 4: 5x−6+6=19+6
Step 5: 5x=25
Step 6: x=5
What property justifies going from step 3 to step 4?
The property that justifies going from step 3 to step 4 is the addition property of equality. According to this property, if you add the same value to both sides of an equation, the equality is still maintained. In step 3, 6 is added to both sides of the equation to isolate the variable term, resulting in step 4 where 6 is added to both sides of the equation.
A student solved the equation: x+2(x+1)=17
Step 1: x+2x+2=17
Step 2: 3x+2=17
Step 3: 3x=15
Step 4: x=45
Identify the property used to arrive at Step 1:
What step includes a mistake made from the previous step?
What should have been the correct answer for x ?
The property used to arrive at Step 1 is the distributive property. In this step, the student distributed the 2 to both terms inside the parentheses.
The mistake is made in Step 4. The student incorrectly divided both sides of the equation by 3 instead of subtracting 2 from both sides.
To find the correct value of x, we need to go back to Step 3 and subtract 2 from both sides of the equation:
Step 3: 3x = 15
Subtract 2 from both sides:
3x - 2 = 15 - 2
3x - 2 = 13
Therefore, the correct answer for x is 13/3.