Answer:
1. [tex]\dfrac{c}{6}-\dfrac{7}{6}[/tex]
2. m
3. 6w
4. 39x + 78
5. 75x - 153
Step-by-step explanation:
1. The product of −2c+14 and the multiplicative inverse of −12 is
[tex](-2c+14)\cdot \dfrac{1}{-12}[/tex]
Use distributive property:
[tex](-2c+14)\cdot \dfrac{1}{-12}\\ \\=-\dfrac{1}{12}\cdot (-2c)-\dfrac{1}{12}\cdot 14\\ \\=\dfrac{c}{6}-\dfrac{7}{6}[/tex]
2. Solve 10+(m−10)
Open the brackets remembering that the sign before brackets is "+":
[tex]10+(m-10)\\ \\=10+m-10[/tex]
Combine the like terms usin commutative property:
[tex]10+m-10\\ \\=(10-10)+m\\ \\=0+m \\ \\=m[/tex]
3. Solve 6w+3−3
Combine the like terms:
[tex]6w+3-3\\ \\=6w+(3-3)\\ \\=6w+0\\ \\=6w[/tex]
4. Write the expression in standard form 13(3x+6).
Use distributive property:
[tex]13(3x+6)\\ \\=13\cdot 3x+13\cdot 6\\ \\=39x+78[/tex]
5. Write the expression in standard form 15(5x−10)−3.
Use distributive property:
[tex]15(5x-10)-3\\ \\=15\cdot 5x-15\cdot 10-3\\ \\=75x-150-3[/tex]
Combine the like terms:
[tex]=75x+(-150-3)\\ \\=75x-(150+3)\\ \\=75x-153[/tex]
