Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(4(6x+5)=-1-(-15+x)\)
2. \(6(4x+2)=-3-(13+x)\)
3. \(6(4x-1)=-9+(10+x)\)
4. \(6(4x-4)=-15+(7+x)\)
5. \(2(4x+2)=4-(-2+x)\)
6. \(2(-4x+6)=7-(-14+x)\)
7. \(5(-6x-3)=-15+(-3+x)\)
8. \(2(-5x-1)=-10+(3+x)\)
9. \(4(-3x-4)=-10+(8+x)\)
10. \(3(-x+3)=9+(-6-5x)\)
11. \(6(-5x-2)=-4+(-2+x)\)
12. \(5(-2x+2)=1-(-9+3x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (6x+5)& = & -1 \color{red}{-} (-15+x) \\\Leftrightarrow & 24x+20& = &-1+15-x \\\Leftrightarrow & 24x \color{red}{+20} & = &14 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 24x+x& = &14-20 \\\Leftrightarrow & 25x& = &-6 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-6}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-6}{25} & & \\ & V = \left\{ \frac{-6}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (4x+2)& = & -3 \color{red}{-} (13+x) \\\Leftrightarrow & 24x+12& = &-3-13-x \\\Leftrightarrow & 24x \color{red}{+12} & = &-16 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-16 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 24x+x& = &-16-12 \\\Leftrightarrow & 25x& = &-28 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-28}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-28}{25} & & \\ & V = \left\{ \frac{-28}{25} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (4x-1)& = & -9 \color{red}{+} (10+x) \\\Leftrightarrow & 24x-6& = &-9+10+x \\\Leftrightarrow & 24x \color{red}{-6} & = &1 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 24x-x& = &1+6 \\\Leftrightarrow & 23x& = &7 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{7}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{7}{23} & & \\ & V = \left\{ \frac{7}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (4x-4)& = & -15 \color{red}{+} (7+x) \\\Leftrightarrow & 24x-24& = &-15+7+x \\\Leftrightarrow & 24x \color{red}{-24} & = &-8 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 24x-x& = &-8+24 \\\Leftrightarrow & 23x& = &16 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{16}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{16}{23} & & \\ & V = \left\{ \frac{16}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (4x+2)& = & 4 \color{red}{-} (-2+x) \\\Leftrightarrow & 8x+4& = &4+2-x \\\Leftrightarrow & 8x \color{red}{+4} & = &6 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 8x+x& = &6-4 \\\Leftrightarrow & 9x& = &2 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{2}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{2}{9} & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-4x+6)& = & 7 \color{red}{-} (-14+x) \\\Leftrightarrow & -8x+12& = &7+14-x \\\Leftrightarrow & -8x \color{red}{+12} & = &21 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &21 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -8x+x& = &21-12 \\\Leftrightarrow & -7x& = &9 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{9}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-9}{7} & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-6x-3)& = & -15 \color{red}{+} (-3+x) \\\Leftrightarrow & -30x-15& = &-15-3+x \\\Leftrightarrow & -30x \color{red}{-15} & = &-18 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &-18 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & -30x-x& = &-18+15 \\\Leftrightarrow & -31x& = &-3 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-3}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{3}{31} & & \\ & V = \left\{ \frac{3}{31} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-5x-1)& = & -10 \color{red}{+} (3+x) \\\Leftrightarrow & -10x-2& = &-10+3+x \\\Leftrightarrow & -10x \color{red}{-2} & = &-7 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & -10x-x& = &-7+2 \\\Leftrightarrow & -11x& = &-5 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-5}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{5}{11} & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-3x-4)& = & -10 \color{red}{+} (8+x) \\\Leftrightarrow & -12x-16& = &-10+8+x \\\Leftrightarrow & -12x \color{red}{-16} & = &-2 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & -12x-x& = &-2+16 \\\Leftrightarrow & -13x& = &14 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{14}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-14}{13} & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-x+3)& = & 9 \color{red}{+} (-6-5x) \\\Leftrightarrow & -3x+9& = &9-6-5x \\\Leftrightarrow & -3x \color{red}{+9} & = &3 \color{red}{-5x} \\\Leftrightarrow & -3x \color{red}{+9} \color{blue}{-9} \color{blue}{+5x} & = &3 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-9} \\\Leftrightarrow & -3x+5x& = &3-9 \\\Leftrightarrow & 2x& = &-6 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{-6}{ \color{red}{2} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-5x-2)& = & -4 \color{red}{+} (-2+x) \\\Leftrightarrow & -30x-12& = &-4-2+x \\\Leftrightarrow & -30x \color{red}{-12} & = &-6 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -30x-x& = &-6+12 \\\Leftrightarrow & -31x& = &6 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{6}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-6}{31} & & \\ & V = \left\{ \frac{-6}{31} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-2x+2)& = & 1 \color{red}{-} (-9+3x) \\\Leftrightarrow & -10x+10& = &1+9-3x \\\Leftrightarrow & -10x \color{red}{+10} & = &10 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+10} \color{blue}{-10} \color{blue}{+3x} & = &10 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-10} \\\Leftrightarrow & -10x+3x& = &10-10 \\\Leftrightarrow & -7x& = &0 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{0}{ \color{red}{-7} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)