ACT 1 Alg: Solve equations and inequalities in 1 variable

Welcome to your ACT 1 Alg: Solve equations and inequalities in 1 variable

$Q_{1}:$ For what values of $x$ is $5x+97=47$?

$\frac{-59}{5}$

$-10$

$10$

$\frac{59}{5}$

$Q_{2}:$ For what values of $x$ is $0.8x-2.3=0.5$?

$3.5$

$-3.5$

$-2.25$

$2.25$

$Q_{3}:$ For what values of $x$ is $0.2x+0.3=1.9$?

$0.33$

$8$

$0.8$

$0.08$

$Q_{4}:$ For what values of $x$ is $\frac{2x}{5}+\frac{6}{5}=5$?

$\frac{19}{2}$

$\frac{31}{2}$

$\frac{19}{5}$

$\frac{31}{5}$

$Q_{5}:$ The solution of $\frac{1}{2}x+3(x-2)=2(x+1)+1$ is

$4$

$6$

$5$

$3$

$Q_{6}:$ If $z$ is an integer and the average (arithmetic mean) of $1, 2, 3$, and $z$ is less than $20$, what is the greatest possible value of $z$?

$73$

$74$

$75$

$73.5$

$Q_{7}: \frac{3}{4}-\frac{5}{x}=\frac{7}{x}$, the value of $x$ is

$48$

$12$

$16$

$8$

$Q_{8}:$ For what value of $y$ is $\frac{3}{4}-\frac{5}{y}>\frac{7}{y}$?

$\left \{ y\mid y >16 \text{ or } y < 0 \right \}$

$ \left \{ y\mid y < 0 \right \} $

$\left \{ y\mid y \leq 0 \text{ or } y \geq 16 \right \}$

$\left \{ y\mid 0 \leq y \leq 16 \right \}$

$Q_{9}:$ For what values of $x$ is $3 \left | x + 5 \right | -5< 7$

$\left \{ x\mid -9

$\left \{ x\mid -9\leq x \leq -1 \right \}$

$\left \{ x\mid x -1 \right \}$

$\left \{ x\mid x\leq -9 \text{ or } x\geq -1 \right \}$

$Q_{10}:$ $ 4(\sqrt[3]{x}+1)=\sqrt[3]{x} +25 $, the value of $x$ is

$144$

$304$

$343$

$7$

$Q_{11}:$ If $\frac{x+3}{2}+3x=5(x-3)+\frac{(x+23)}{5}$ , what is the value of $x$?

$3$

$5$

$7$

$9$

$Q_{12}:$ If $ax - b = c - dx$, what is the value of $x$ in terms of $a, b, c,$ and $d$ ?

$\frac{b+c}{a+d}$

$\frac{c-d}{a-d}$

$\frac{b+c-d}{a}$

$\frac{c}{b} - \frac{d}{a}$

$Q_{13}:$ Which of the following inequalities is equivalent to $0.6( y-7) - 0.3y > 1.8 +0.9y$ ?

$y<10$

$y<-10$

$y>10$

$y>-10$

$Q_{14}:$ One half of a number decreased by $3$ is at most $−5$. Which of the following inequalities represents the statement?

$\frac{n}{2}-3\leq -5$

$3- \frac{n}{2} \leq -5$

$\frac{n}{2}-3< -5$

$3- \frac{n}{2} < -5$

$Q_{15}:$Which of the following numbers is NOT a solution to the inequality $\frac{(3b+5)}{-2}\geq (b-8)$ ?

$0$

$1$

$2$

$3$

$Q_{16}:$ Nine is not more than the sum of a number and 17. Which of the following inequalities represents the statement?

$9\geq 17w$

$9 \geq w+17$

$9\leq 17w$

$9 \leq w+17$

$Q_{17}:$ Four times the greatest of three consecutive odd integers exceeds three times the least by 31. What is the greatest of the three consecutive odd integers?

$15$

$19$

$16$

$13$

$Q_{18}:$ The sum of four consecutive odd integers is 296 . What is the greatest of the four consecutive odd integers?

$77$

$78$

$79$

$80$

$Q_{19}:$ Eight less than four times the number $t$ is twenty. What is the value of $t$?

$4$

$5$

$6$

$7$

$Q_{20}:$ A number $K$ is decreased by $23$ and then multiplied by $\frac{1}{2}$. The result is $8$ more than twice the number $K$.

$-13$

$\frac{-34}{3}$

$\frac{-29}{3}$

$-8$

$Q_{21}:$ There are one hundred forty-two students in a high school band. These students represent two ninth of the total students in the high school. How many students attend the school?

$639$

$613$

$587$

$665$

$Q_{22}:$ A $48£$ shirts costs $22£$ more than one half the cost of a pair of pants. How much does the pair of pants cost?

$52£$

$50£$

$48£$

$40£$

$Q_{23}: \frac{(15-6y)}{3}=5-ay$ . If the linear equation is an identity, what is the value of a ?

$2$

$3$

$4$

$5$

$Q_{24}: 4h+13=7(h-2)+dh $ If the linear equation has no solution, which of the following could be the value of $d$ ?

$-1$

$-2$

$-3$

$-4$

$Q_{25}:$ Ayah Car Rental charges a flat fee of $40.00£$ per day plus $0.54£$ per mile to rent a car. Malk Car Rental charges a flat fee of $65.00£$ per day plus $0.36£$ per mile to rent a car. If a car is rented for three days, at least how many miles would you have to drive, to the nearest mile, to make the Ayah Car Rental company the better option?

$416$ miles

$471$ miles

$417$ miles

$415$ miles

$Q_{26}:$ The number of students in a Math class is four fifths the number of students in a English class. The total number of students in both classes does not exceed 54. What is the greatest possible number of students in the English class?

$30$

$32$

$34$

$36$

$Q_{27}:$ Which of the following inequalities represents the same set as the set graphed on the number line shown?

$0 < x < 3 $

$0 \leq x \leq 3 $

$0 \leq x < 3 $

$0 < x \leq 3 $

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