This will be more of a mini-lesson due to this being a very small concept, but it's still good to know regardless, due to it helping transition from one to two-step equations as well as helping give a better understanding of variables. In these equations, values will be given to you (such as x=1), and then you will plug the value into the equation and calculating the value of the expression, utilizing PEMDAS.
1: Evaluate 2x-4y if x=12 and y=4
Firstly, variables x and y can be substituted with 12 and y, making the expression 2(12)-4(4).
Next, 2 and 12 as well as -4 and 4 can be multiplied due to an assumed multiplication between the value directly next to a parentheses and the value inside, simplifying the expression to 24-16.
Finally, 16 can be subtracted from 24 to get the final answer of 8.
Answer: 8
2: Evaluate 9x+13y if x=-4 and y=13
First, -4 and 13 can substitute their respective variables, making the expression 9(-4)+13(13).
Secondly, -4 will be multiplied with 9 to get the product of -36, and 13 will be multiplied by itself (could also be written as 13²) to get 169, simplifying the expression to -36+169, also known as 169-36.
Finally, 36 can be subtracted from 169 (or 169 can be added to -36) to get the final sum of 133.
Answer: 133
3: Evaluate 5x³+y if x=3 and y=8
Firstly, 3 and 8 will substitute x and y, respectively, changing the expression to 5(3)³+8.
Next, 3 will be cubed due to exponents being the first step in PEMDAS that applies to the equation, simplifying the equation to 5(27)+8.
27 will then be multiplied by 5, creating the product of 135. Finally, 8 will be added to 135, giving the final answer of 143.
Answer: 143
4: Evaluate x²+8y if x=-4 and y=-2
Firstly, -4 and -2 can substitute their respective exponents, now making the expression (-4)²+8(-2).
A common mistake made when squaring a negative number is keeping it as a negative number, but in this case -4 squared will equal 16 due to the entire -4 being in parentheses. However, if -4 was not in parentheses, it would equal -16 because of an assumed negative one multiplying the 4, therefore meaning it would be -(4)². Additionally, 8 will be multiplied by -2 to get the product of -16, making the expression 16-16.
Finally, -16 will simply cancel out 16 to get the final answer of 0.
Answer: 0
5: Evaluate 5x²÷3y if x=-5 and y=5
First of all, -5 and 5 will be substituted into the equation, making the expression 5(-5)²÷3(5).
Next, the -5 will be squared to get 25 and then multiplied by 5, making the product 125. After that, the 3 and 5 will get multiplied, making the product 15. The division symbol between the two wouldn't be used before the 3 and 5 being multiplied due to the 5 being in parentheses, and it could also be looked at like 5(-5)² being the numerator and 3(5) being the denominator in a fraction.
Finally, 125 will be divided by 15, giving the final answer of 8.33.
Answer: 8.33
6: Evaluate 2√x·9y if x=9 and y=0.5
After substituting the variables with their given values, the equation is now 2√9·9(0.5).
Firstly, 9 has a perfect square root, so it can easily be found, simplifying it to 2(3)·9(0.5). Next, 2 can be multiplied by 3, and 9 can be multiplied by 0.5, further simplifying the expression to 6·4.5.
Finally, 6 can be multiplied by 4.5 to get the answer of 27.
Answer: 27
7: Evaluate 3.5x³÷y² if x=5 and y=10
First and foremost, the variables will be substituted with the values given, creating the expression 3.5(5)³÷10².
Secondly, 5 will be cubed, and 10 will be squared due to exponents being the first step of PEMDAS in this expression, making it 3.5(125)÷100.
Next, multiplication and division will be done from left to right, with 3.5 multiplying by 125 to get the product of 437.5, and 437.5 finally being divided by 100 to get the answer of 4.375.
Answer: 4.375
8: Evaluate 13∛x+4y if x=-27 and y=0
As usual, variables x and y will be replaced with their respective values of -27 and 0, making the expression 13∛-27+4(0).
Since a cube root still falls in the same field as an exponent, that will be done next. While the square root of a negative number is imaginary, a cube root is simply negative, with ∛-27 being -3 due to -3·-3·-3 equaling -27.
The expression has been simplified down to 13(-3)+4(0), and multiplication will be done further simplifying it to -39+0, and since adding 0 does not change -39 at all, that will be the final answer.
Answer: -39
1: Evaluate 9x-4y if x=2 and y=-4
2: Evaluate 5.75x+10y if x=40 and y=-13
3: Evaluate -8y+ˣ⁄₃ if x=3 and y=1
4: Evaluate -5x+y² if x=-5 and y=-2
5: Evaluate √x+2y³ if x=36 and y=4
6: Evaluate ∛y+9ˣ⁄₃ if x=1 and y=-8
7: Evaluate -4x²÷2y if x=5 and y=-2.5
8: Evaluate 12x³√y if x=3 and y=0.36
9: Evaluate -6.5x²÷2√y if x=5 and y=36
10: Evaluate 19y+√4x³ if x=4 and y=0.5
1: 34
2: 100
3: -7
4: 29
5: 134
6: 1
7: 20
8: 194.4
9: -13.54
10: 25.5