Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(4(6x+3)=-8+(-6+x)\)
2. \(4(x+7)=14-(-3+x)\)
3. \(2(2x+4)=6-(-6+3x)\)
4. \(2(4x+6)=-4+(-7+x)\)
5. \(2(-6x+7)=-1-(-14+x)\)
6. \(4(2x+5)=13+(-12+x)\)
7. \(4(-4x-4)=-10+(-8+3x)\)
8. \(2(-6x+2)=-6-(6+x)\)
9. \(3(-5x-5)=1+(-2-2x)\)
10. \(2(3x+5)=4-(11-5x)\)
11. \(5(-4x-3)=4+(5+x)\)
12. \(4(-2x-2)=-3-(-9+x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (6x+3)& = & -8 \color{red}{+} (-6+x) \\\Leftrightarrow & 24x+12& = &-8-6+x \\\Leftrightarrow & 24x \color{red}{+12} & = &-14 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 24x-x& = &-14-12 \\\Leftrightarrow & 23x& = &-26 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-26}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-26}{23} & & \\ & V = \left\{ \frac{-26}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (x+7)& = & 14 \color{red}{-} (-3+x) \\\Leftrightarrow & 4x+28& = &14+3-x \\\Leftrightarrow & 4x \color{red}{+28} & = &17 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & 4x+x& = &17-28 \\\Leftrightarrow & 5x& = &-11 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-11}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-11}{5} & & \\ & V = \left\{ \frac{-11}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (2x+4)& = & 6 \color{red}{-} (-6+3x) \\\Leftrightarrow & 4x+8& = &6+6-3x \\\Leftrightarrow & 4x \color{red}{+8} & = &12 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+8} \color{blue}{-8} \color{blue}{+3x} & = &12 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-8} \\\Leftrightarrow & 4x+3x& = &12-8 \\\Leftrightarrow & 7x& = &4 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{4}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{4}{7} & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (4x+6)& = & -4 \color{red}{+} (-7+x) \\\Leftrightarrow & 8x+12& = &-4-7+x \\\Leftrightarrow & 8x \color{red}{+12} & = &-11 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 8x-x& = &-11-12 \\\Leftrightarrow & 7x& = &-23 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-23}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-23}{7} & & \\ & V = \left\{ \frac{-23}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-6x+7)& = & -1 \color{red}{-} (-14+x) \\\Leftrightarrow & -12x+14& = &-1+14-x \\\Leftrightarrow & -12x \color{red}{+14} & = &13 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+14} \color{blue}{-14} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{-14} \\\Leftrightarrow & -12x+x& = &13-14 \\\Leftrightarrow & -11x& = &-1 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-1}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{1}{11} & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (2x+5)& = & 13 \color{red}{+} (-12+x) \\\Leftrightarrow & 8x+20& = &13-12+x \\\Leftrightarrow & 8x \color{red}{+20} & = &1 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 8x-x& = &1-20 \\\Leftrightarrow & 7x& = &-19 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-19}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-19}{7} & & \\ & V = \left\{ \frac{-19}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-4x-4)& = & -10 \color{red}{+} (-8+3x) \\\Leftrightarrow & -16x-16& = &-10-8+3x \\\Leftrightarrow & -16x \color{red}{-16} & = &-18 \color{red}{+3x} \\\Leftrightarrow & -16x \color{red}{-16} \color{blue}{+16} \color{blue}{-3x} & = &-18 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+16} \\\Leftrightarrow & -16x-3x& = &-18+16 \\\Leftrightarrow & -19x& = &-2 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-2}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{2}{19} & & \\ & V = \left\{ \frac{2}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-6x+2)& = & -6 \color{red}{-} (6+x) \\\Leftrightarrow & -12x+4& = &-6-6-x \\\Leftrightarrow & -12x \color{red}{+4} & = &-12 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -12x+x& = &-12-4 \\\Leftrightarrow & -11x& = &-16 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-16}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{16}{11} & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-5x-5)& = & 1 \color{red}{+} (-2-2x) \\\Leftrightarrow & -15x-15& = &1-2-2x \\\Leftrightarrow & -15x \color{red}{-15} & = &-1 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{-15} \color{blue}{+15} \color{blue}{+2x} & = &-1 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+15} \\\Leftrightarrow & -15x+2x& = &-1+15 \\\Leftrightarrow & -13x& = &14 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{14}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-14}{13} & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (3x+5)& = & 4 \color{red}{-} (11-5x) \\\Leftrightarrow & 6x+10& = &4-11+5x \\\Leftrightarrow & 6x \color{red}{+10} & = &-7 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+10} \color{blue}{-10} \color{blue}{-5x} & = &-7 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-10} \\\Leftrightarrow & 6x-5x& = &-7-10 \\\Leftrightarrow & x& = &-17 \\ & V = \left\{ -17 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-4x-3)& = & 4 \color{red}{+} (5+x) \\\Leftrightarrow & -20x-15& = &4+5+x \\\Leftrightarrow & -20x \color{red}{-15} & = &9 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & -20x-x& = &9+15 \\\Leftrightarrow & -21x& = &24 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{24}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-8}{7} & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-2x-2)& = & -3 \color{red}{-} (-9+x) \\\Leftrightarrow & -8x-8& = &-3+9-x \\\Leftrightarrow & -8x \color{red}{-8} & = &6 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & -8x+x& = &6+8 \\\Leftrightarrow & -7x& = &14 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{14}{ \color{red}{-7} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)