# Vgln. eerste graad (reeks 3)

#### Reeks met haakjes

1. $$5(-x-1)=-2+(-10-2x)$$
2. $$6(x-7)=-8+(2+x)$$
3. $$3(2x+4)=-1+(-4+5x)$$
4. $$4(6x+6)=-7+(-15+x)$$
5. $$3(5x-1)=3+(-11+4x)$$
6. $$6(-2x-5)=6-(-8+5x)$$
7. $$2(-3x+6)=-11+(4-5x)$$
8. $$4(2x+5)=5+(8+x)$$
9. $$2(-2x-7)=-7-(-5-3x)$$
10. $$4(-3x+4)=15+(7+5x)$$
11. $$4(6x-3)=4-(-10+x)$$
12. $$3(-6x-2)=-10+(3+5x)$$

#### Reeks met haakjes

##### Verbetersleutel

1. \begin{align} & \color{red}{5} (-x-1)& = & -2 \color{red}{+} (-10-2x) \\\Leftrightarrow & -5x-5& = &-2-10-2x \\\Leftrightarrow & -5x \color{red}{-5} & = &-12 \color{red}{-2x} \\\Leftrightarrow & -5x \color{red}{-5} \color{blue}{+5} \color{blue}{+2x} & = &-12 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+5} \\\Leftrightarrow & -5x+2x& = &-12+5 \\\Leftrightarrow & -3x& = &-7 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-7}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{7}{3} & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}
2. \begin{align} & \color{red}{6} (x-7)& = & -8 \color{red}{+} (2+x) \\\Leftrightarrow & 6x-42& = &-8+2+x \\\Leftrightarrow & 6x \color{red}{-42} & = &-6 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & 6x-x& = &-6+42 \\\Leftrightarrow & 5x& = &36 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{36}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{36}{5} & & \\ & V = \left\{ \frac{36}{5} \right\} & \\\end{align}
3. \begin{align} & \color{red}{3} (2x+4)& = & -1 \color{red}{+} (-4+5x) \\\Leftrightarrow & 6x+12& = &-1-4+5x \\\Leftrightarrow & 6x \color{red}{+12} & = &-5 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &-5 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & 6x-5x& = &-5-12 \\\Leftrightarrow & x& = &-17 \\ & V = \left\{ -17 \right\} & \\\end{align}
4. \begin{align} & \color{red}{4} (6x+6)& = & -7 \color{red}{+} (-15+x) \\\Leftrightarrow & 24x+24& = &-7-15+x \\\Leftrightarrow & 24x \color{red}{+24} & = &-22 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-22 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 24x-x& = &-22-24 \\\Leftrightarrow & 23x& = &-46 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-46}{ \color{red}{23} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}
5. \begin{align} & \color{red}{3} (5x-1)& = & 3 \color{red}{+} (-11+4x) \\\Leftrightarrow & 15x-3& = &3-11+4x \\\Leftrightarrow & 15x \color{red}{-3} & = &-8 \color{red}{+4x} \\\Leftrightarrow & 15x \color{red}{-3} \color{blue}{+3} \color{blue}{-4x} & = &-8 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+3} \\\Leftrightarrow & 15x-4x& = &-8+3 \\\Leftrightarrow & 11x& = &-5 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-5}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-5}{11} & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}
6. \begin{align} & \color{red}{6} (-2x-5)& = & 6 \color{red}{-} (-8+5x) \\\Leftrightarrow & -12x-30& = &6+8-5x \\\Leftrightarrow & -12x \color{red}{-30} & = &14 \color{red}{-5x} \\\Leftrightarrow & -12x \color{red}{-30} \color{blue}{+30} \color{blue}{+5x} & = &14 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+30} \\\Leftrightarrow & -12x+5x& = &14+30 \\\Leftrightarrow & -7x& = &44 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{44}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-44}{7} & & \\ & V = \left\{ \frac{-44}{7} \right\} & \\\end{align}
7. \begin{align} & \color{red}{2} (-3x+6)& = & -11 \color{red}{+} (4-5x) \\\Leftrightarrow & -6x+12& = &-11+4-5x \\\Leftrightarrow & -6x \color{red}{+12} & = &-7 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+12} \color{blue}{-12} \color{blue}{+5x} & = &-7 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-12} \\\Leftrightarrow & -6x+5x& = &-7-12 \\\Leftrightarrow & -x& = &-19 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-19}{ \color{red}{-1} } \\\Leftrightarrow & x = 19 & & \\ & V = \left\{ 19 \right\} & \\\end{align}
8. \begin{align} & \color{red}{4} (2x+5)& = & 5 \color{red}{+} (8+x) \\\Leftrightarrow & 8x+20& = &5+8+x \\\Leftrightarrow & 8x \color{red}{+20} & = &13 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 8x-x& = &13-20 \\\Leftrightarrow & 7x& = &-7 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-7}{ \color{red}{7} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}
9. \begin{align} & \color{red}{2} (-2x-7)& = & -7 \color{red}{-} (-5-3x) \\\Leftrightarrow & -4x-14& = &-7+5+3x \\\Leftrightarrow & -4x \color{red}{-14} & = &-2 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-14} \color{blue}{+14} \color{blue}{-3x} & = &-2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+14} \\\Leftrightarrow & -4x-3x& = &-2+14 \\\Leftrightarrow & -7x& = &12 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{12}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-12}{7} & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}
10. \begin{align} & \color{red}{4} (-3x+4)& = & 15 \color{red}{+} (7+5x) \\\Leftrightarrow & -12x+16& = &15+7+5x \\\Leftrightarrow & -12x \color{red}{+16} & = &22 \color{red}{+5x} \\\Leftrightarrow & -12x \color{red}{+16} \color{blue}{-16} \color{blue}{-5x} & = &22 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-16} \\\Leftrightarrow & -12x-5x& = &22-16 \\\Leftrightarrow & -17x& = &6 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{6}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-6}{17} & & \\ & V = \left\{ \frac{-6}{17} \right\} & \\\end{align}
11. \begin{align} & \color{red}{4} (6x-3)& = & 4 \color{red}{-} (-10+x) \\\Leftrightarrow & 24x-12& = &4+10-x \\\Leftrightarrow & 24x \color{red}{-12} & = &14 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 24x+x& = &14+12 \\\Leftrightarrow & 25x& = &26 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{26}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{26}{25} & & \\ & V = \left\{ \frac{26}{25} \right\} & \\\end{align}
12. \begin{align} & \color{red}{3} (-6x-2)& = & -10 \color{red}{+} (3+5x) \\\Leftrightarrow & -18x-6& = &-10+3+5x \\\Leftrightarrow & -18x \color{red}{-6} & = &-7 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{-6} \color{blue}{+6} \color{blue}{-5x} & = &-7 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+6} \\\Leftrightarrow & -18x-5x& = &-7+6 \\\Leftrightarrow & -23x& = &-1 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-1}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{1}{23} & & \\ & V = \left\{ \frac{1}{23} \right\} & \\\end{align}
Oefeningengenerator vanhoeckes.be/wiskunde 2024-08-09 04:04:43