2-step Equations
2-Step Equations (distributive Prop.)
2-step Inequalities
2-Step Inequalities with Negative Coefficients
ALLUM
100
Ms. Williams checks a receipt from the gym and notices that the total charge was $14 after a $6 discount was applied. The receipt also shows that each visit costs the same amount. How many times did Jordan go to the gym?
Equation: 4x−6=14
Answer: x=5
100
Dr. Rucker looks at her movie receipt and see that the total cost was $15. Each ticket had the same base price, but an additional $2 fee was added to every ticket. Dr. Rucker bought three tickets. What was the base price of one ticket?
100
Coach Moe wants to qualify for a competition that requires at least 11 total practice hours. Her practice time is evaluated by doubling the number of hours she practices and then increasing 3 more hours. How many hours must Coach Moe practice?
100
A submarine’s depth is recorded using a system that finds the product of the depth and −2 and then increases by 4. If the recorded value must remain below 10 meters, what depths are possible?
100
Ms. Terri reviews her pay statement and sees that her hourly earnings were adjusted by adding $9. Her pay rate is $3 per hour. After all adjustments, the final amount shown is -$3. How many hours did Ms. Terri work?
200
Dr. Gordian compares two temperature readings taken several hours apart. The second reading was found by first doubling the original temperature and then increasing it by 3 degrees. If the second reading is −5°C, what was the original temperature?
Equation: 2x+3=−5
Answer: x=−4∘C
200
Mrs. Veith conducts a science experiment where a freezer changes the temperature of an object based on a rule. The rule first combines 4 degrees to the starting temperature and then multiplies the result by −2. The final temperature change is −12°C. What was the starting temperature?
200
Mr. Winn is scuba diving and must remain within a safe depth range. A safety check divides his depth by 4 and then adjusting downward 2 meters. If the result must stay below 1 meter, how deep can Mr. Winn dive?
200
Ms. Hill’s debt is evaluated her debt by finding the product of 3 and the amount she owes and increasing by 5. To meet repayment conditions, the result must be more than −20. What debt amounts satisfy this condition?
3x+5=-20
x<8.33
200
A machine operated by Coach B functions safely only when a temperature rule is satisfied. The rule doubles the temperature after after finding the difference from 4. The result must be less than 6. What temperatures keep the machine operating safely?
300
Coach Lozada planned a run by breaking the main portion of his route into five equal parts and later extending the run by 7 miles. When he finishes, the total distance is 9 miles. What was the length of each equal part?
x/5 + 7 = 9
x= 10
5 miles per part
300
Mrs. Adcock noticed that a charge applied to her bank balance resulted in $10. The charge shows a difference between the balance and $1.50 from her balance and then multiplies the result by 4. What was Mrs. Adcock's original balance?
300
Mrs. Linn wants to avoid an overdraft fee. The bank evaluates her account by find the product of the balance and 5 and then decreasing by $7. The result must be greater than −$2. What balances meet this requirement?
300
During a weather study, a temperature reading is found by finding the product of −4 and then increasing by 6. For safety reasons, the final value must be at least −2. What temperatures are acceptable?
300
Dr. Murray tracks a stock whose value was changed using a formula finds the product of the original value by −4 and then increase by 1. The final change recorded was −11. What was the original value of the stock?
400
Mr. Daniels reviews his bank statement and notices that after spending $5, the remaining balance is −$3. The statement also shows that this remaining balance represents half of what he originally had. How much money did Mr. Daniels start with?
400
Mr. Jenkins receives a test score that was processed through a grading formula. The formula finds the sum of 6 and the score and then takes half of the result, producing −2. What score did Mr. Jenkins receive?
400
Mr. Logan runs a science experiment where a temperature is adjusted by taking half of the original value and then increasing by 6 degrees. For the experiment to work, the final value cannot exceed 4 degrees. What temperatures are allowed?
400
A calculation takes negative one-half of a number and then increases by 3. The result must be no greater than 1. What values satisfy this condition?
400
An underwater drone’s depth is processed by splitting the depth by 2 and then ascending 5. The final value must be at least 1. What depths are possible?
500
A research team analyzes data from a submarine’s dive. The submarine moved downward at a constant rate of 3 meters per second and later rose 4.5 meters. The final recorded depth was −10.5 meters. For how long did the submarine descend?
500
Mr. Whitehead reviews a debt that has combined sum of −3 and the amount he owes. Then multiplied the result by 5. The final value is 20. What was the original amount of Mr. Whitehead’s debt?
5(x-3)=20
x=7
500
Mr. P’s score is processed by finding the difference of the original score and 3, then doubling the result. The final score must be no more than 8. What original scores are possible?
500
During a science lab, a sensor evaluates a chemical mixture using a specific rule. The rule first determines the sum of the measured value and 2, and then scales the entire quantity using a factor of −5. For the mixture to be considered safe, the final value must be greater than or equal to −15.
What values of the measured amount satisfy this condition?
500
Mr. Alouch’s test score is evaluated by determining the difference of 2 from the score and the product of the result and 3. The final value must be no greater than −6. What scores could Mr. Alouch have earned?
