Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-6x+6)& = & 4 \color{red}{-} (6+x) \\\Leftrightarrow & -12x+12& = &4-6-x \\\Leftrightarrow & -12x \color{red}{+12} & = &-2 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -12x+x& = &-2-12 \\\Leftrightarrow & -11x& = &-14 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-14}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{14}{11} & & \\ & V = \left\{ \frac{14}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (5x-3)& = & -9 \color{red}{-} (13-3x) \\\Leftrightarrow & 25x-15& = &-9-13+3x \\\Leftrightarrow & 25x \color{red}{-15} & = &-22 \color{red}{+3x} \\\Leftrightarrow & 25x \color{red}{-15} \color{blue}{+15} \color{blue}{-3x} & = &-22 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+15} \\\Leftrightarrow & 25x-3x& = &-22+15 \\\Leftrightarrow & 22x& = &-7 \\\Leftrightarrow & \frac{22x}{ \color{red}{22} }& = &\frac{-7}{ \color{red}{22} } \\\Leftrightarrow & x = \frac{-7}{22} & & \\ & V = \left\{ \frac{-7}{22} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-x+4)& = & -1 \color{red}{-} (-13-4x) \\\Leftrightarrow & -5x+20& = &-1+13+4x \\\Leftrightarrow & -5x \color{red}{+20} & = &12 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{+20} \color{blue}{-20} \color{blue}{-4x} & = &12 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-20} \\\Leftrightarrow & -5x-4x& = &12-20 \\\Leftrightarrow & -9x& = &-8 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-8}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{8}{9} & & \\ & V = \left\{ \frac{8}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-x-2)& = & -6 \color{red}{+} (12+4x) \\\Leftrightarrow & -5x-10& = &-6+12+4x \\\Leftrightarrow & -5x \color{red}{-10} & = &6 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{-10} \color{blue}{+10} \color{blue}{-4x} & = &6 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+10} \\\Leftrightarrow & -5x-4x& = &6+10 \\\Leftrightarrow & -9x& = &16 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{16}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-16}{9} & & \\ & V = \left\{ \frac{-16}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (x-7)& = & -2 \color{red}{+} (-1-5x) \\\Leftrightarrow & 6x-42& = &-2-1-5x \\\Leftrightarrow & 6x \color{red}{-42} & = &-3 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-42} \color{blue}{+42} \color{blue}{+5x} & = &-3 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+42} \\\Leftrightarrow & 6x+5x& = &-3+42 \\\Leftrightarrow & 11x& = &39 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{39}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{39}{11} & & \\ & V = \left\{ \frac{39}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-6x+2)& = & 15 \color{red}{-} (-5+x) \\\Leftrightarrow & -24x+8& = &15+5-x \\\Leftrightarrow & -24x \color{red}{+8} & = &20 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -24x+x& = &20-8 \\\Leftrightarrow & -23x& = &12 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{12}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-12}{23} & & \\ & V = \left\{ \frac{-12}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (x-7)& = & -12 \color{red}{+} (2+3x) \\\Leftrightarrow & 2x-14& = &-12+2+3x \\\Leftrightarrow & 2x \color{red}{-14} & = &-10 \color{red}{+3x} \\\Leftrightarrow & 2x \color{red}{-14} \color{blue}{+14} \color{blue}{-3x} & = &-10 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+14} \\\Leftrightarrow & 2x-3x& = &-10+14 \\\Leftrightarrow & -x& = &4 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{4}{ \color{red}{-1} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-6x-6)& = & -6 \color{red}{-} (-14+x) \\\Leftrightarrow & -12x-12& = &-6+14-x \\\Leftrightarrow & -12x \color{red}{-12} & = &8 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -12x+x& = &8+12 \\\Leftrightarrow & -11x& = &20 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{20}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-20}{11} & & \\ & V = \left\{ \frac{-20}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-4x+5)& = & 8 \color{red}{+} (9+x) \\\Leftrightarrow & -24x+30& = &8+9+x \\\Leftrightarrow & -24x \color{red}{+30} & = &17 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &17 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -24x-x& = &17-30 \\\Leftrightarrow & -25x& = &-13 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-13}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{13}{25} & & \\ & V = \left\{ \frac{13}{25} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (x+7)& = & -9 \color{red}{+} (-8+x) \\\Leftrightarrow & 2x+14& = &-9-8+x \\\Leftrightarrow & 2x \color{red}{+14} & = &-17 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{+14} \color{blue}{-14} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{-14} \\\Leftrightarrow & 2x-x& = &-17-14 \\\Leftrightarrow & x& = &-31 \\ & V = \left\{ -31 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (4x-1)& = & -9 \color{red}{+} (7+x) \\\Leftrightarrow & 12x-3& = &-9+7+x \\\Leftrightarrow & 12x \color{red}{-3} & = &-2 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & 12x-x& = &-2+3 \\\Leftrightarrow & 11x& = &1 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{1}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{1}{11} & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (x+5)& = & 1 \color{red}{-} (-11+x) \\\Leftrightarrow & 3x+15& = &1+11-x \\\Leftrightarrow & 3x \color{red}{+15} & = &12 \color{red}{-x} \\\Leftrightarrow & 3x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & 3x+x& = &12-15 \\\Leftrightarrow & 4x& = &-3 \\\Leftrightarrow & \frac{4x}{ \color{red}{4} }& = &\frac{-3}{ \color{red}{4} } \\\Leftrightarrow & x = \frac{-3}{4} & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)