Substitution — Practice Problems and Worked Solutions

17 worked problems

Every step is generated and checked by a computer algebra system.

1. 1.

   Substitute the value and follow the order of operations.

   $$x^2+1\text{when }x=3$$

   Answer: $10$

   Step-by-step solution

   1. $$\text{First replace }x\text{ with }3.$$
   2. $$\text{Evaluate parentheses and powers before addition or subtraction.}$$
   3. $$=10$$
2. 2.

   Substitute the value and follow the order of operations.

   $$2x^2-3\text{when }x=2$$

   Answer: $5$

   Step-by-step solution

   1. $$\text{First replace }x\text{ with }2.$$
   2. $$\text{Evaluate parentheses and powers before addition or subtraction.}$$
   3. $$=5$$
3. 3.

   Substitute the value and follow the order of operations.

   $${\left(x+2\right)}^2\text{when }x=1$$

   Answer: $9$

   Step-by-step solution

   1. $$\text{First replace }x\text{ with }1.$$
   2. $$\text{Evaluate parentheses and powers before addition or subtraction.}$$
   3. $$=9$$
4. 4.

   Substitute the value and follow the order of operations.

   $$3x-1\text{when }x=4$$

   Answer: $11$

   Step-by-step solution

   1. $$\text{First replace }x\text{ with }4.$$
   2. $$\text{Evaluate parentheses and powers before addition or subtraction.}$$
   3. $$=11$$
5. 5.

   Substitute the value and follow the order of operations.

   $$x^2-2x+1\text{when }x=-2$$

   Answer: $9$

   Step-by-step solution

   1. $$\text{First replace }x\text{ with }-2.$$
   2. $$\text{Evaluate parentheses and powers before addition or subtraction.}$$
   3. $$=9$$
6. 6.

   Substitute the value and follow the order of operations.

   $$2{\left(x+3\right)}^2-1\text{when }x=-1$$

   Answer: $7$

   Step-by-step solution

   1. $$\text{First replace }x\text{ with }-1.$$
   2. $$\text{Evaluate parentheses and powers before addition or subtraction.}$$
   3. $$=7$$
7. 7.

   Substitute the value and follow the order of operations.

   $$x^2+3\text{when }x=4$$

   Answer: $19$

   Step-by-step solution

   1. $$\text{First replace }x\text{ with }4.$$
   2. $$\text{Evaluate parentheses and powers before addition or subtraction.}$$
   3. $$=19$$
8. 8.

   Substitute the value and follow the order of operations.

   $$3x^2-2\text{when }x=3$$

   Answer: $25$

   Step-by-step solution

   1. $$\text{First replace }x\text{ with }3.$$
   2. $$\text{Evaluate parentheses and powers before addition or subtraction.}$$
   3. $$=25$$
9. 9.

   Substitute the value and follow the order of operations.

   $${\left(x+1\right)}^2\text{when }x=2$$

   Answer: $9$

   Step-by-step solution

   1. $$\text{First replace }x\text{ with }2.$$
   2. $$\text{Evaluate parentheses and powers before addition or subtraction.}$$
   3. $$=9$$
10. 10.

    Substitute the value and follow the order of operations.

    $$2x-1\text{when }x=6$$

    Answer: $11$

    Step-by-step solution

    1. $$\text{First replace }x\text{ with }6.$$
    2. $$\text{Evaluate parentheses and powers before addition or subtraction.}$$
    3. $$=11$$
11. 11.

    Substitute the value and follow the order of operations.

    $$x^2+4x+4\text{when }x=-3$$

    Answer: $1$

    Step-by-step solution

    1. $$\text{First replace }x\text{ with }-3.$$
    2. $$\text{Evaluate parentheses and powers before addition or subtraction.}$$
    3. $$=1$$
12. 12.

    Substitute the value and follow the order of operations.

    $$3{\left(x+2\right)}^2-4\text{when }x=-1$$

    Answer: $-1$

    Step-by-step solution

    1. $$\text{First replace }x\text{ with }-1.$$
    2. $$\text{Evaluate parentheses and powers before addition or subtraction.}$$
    3. $$=-1$$
13. 13.

    Substitute the value and follow the order of operations.

    $$x^2-5\text{when }x=5$$

    Answer: $20$

    Step-by-step solution

    1. $$\text{First replace }x\text{ with }5.$$
    2. $$\text{Evaluate parentheses and powers before addition or subtraction.}$$
    3. $$=20$$
14. 14.

    Substitute the value and follow the order of operations.

    $$4x^2+x\text{when }x=2$$

    Answer: $18$

    Step-by-step solution

    1. $$\text{First replace }x\text{ with }2.$$
    2. $$\text{Evaluate parentheses and powers before addition or subtraction.}$$
    3. $$=18$$
15. 15.

    Substitute the value and follow the order of operations.

    $${\left(x-4\right)}^2\text{when }x=1$$

    Answer: $9$

    Step-by-step solution

    1. $$\text{First replace }x\text{ with }1.$$
    2. $$\text{Evaluate parentheses and powers before addition or subtraction.}$$
    3. $$=9$$
16. 16.

    Substitute the value and follow the order of operations.

    $$2x^2-3x\text{when }x=-2$$

    Answer: $14$

    Step-by-step solution

    1. $$\text{First replace }x\text{ with }-2.$$
    2. $$\text{Evaluate parentheses and powers before addition or subtraction.}$$
    3. $$=14$$
17. 17.

    Substitute the value and follow the order of operations.

    $$5x+2\text{when }x=7$$

    Answer: $37$

    Step-by-step solution

    1. $$\text{First replace }x\text{ with }7.$$
    2. $$\text{Evaluate parentheses and powers before addition or subtraction.}$$
    3. $$=37$$

More from Math Foundations

• Order of Operations
• Signed Numbers
• Fraction Sense
• Ratios and Percentages
• Exponents and Roots
• Algebraic Expressions
• Linear Equations
• Polynomial Basics
• Inequalities
• Coordinate Plane
• Reading Graphs
• Function Machines
• Factoring Basics