Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-2x-4)& = & -3 \color{red}{-} (-1+x) \\\Leftrightarrow & -12x-24& = &-3+1-x \\\Leftrightarrow & -12x \color{red}{-24} & = &-2 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -12x+x& = &-2+24 \\\Leftrightarrow & -11x& = &22 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{22}{ \color{red}{-11} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (6x+4)& = & -14 \color{red}{+} (-9+x) \\\Leftrightarrow & 12x+8& = &-14-9+x \\\Leftrightarrow & 12x \color{red}{+8} & = &-23 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-23 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 12x-x& = &-23-8 \\\Leftrightarrow & 11x& = &-31 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-31}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-31}{11} & & \\ & V = \left\{ \frac{-31}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-5x-3)& = & -12 \color{red}{+} (2+x) \\\Leftrightarrow & -30x-18& = &-12+2+x \\\Leftrightarrow & -30x \color{red}{-18} & = &-10 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & -30x-x& = &-10+18 \\\Leftrightarrow & -31x& = &8 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{8}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-8}{31} & & \\ & V = \left\{ \frac{-8}{31} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-4x-5)& = & -4 \color{red}{-} (-13+x) \\\Leftrightarrow & -12x-15& = &-4+13-x \\\Leftrightarrow & -12x \color{red}{-15} & = &9 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & -12x+x& = &9+15 \\\Leftrightarrow & -11x& = &24 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{24}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-24}{11} & & \\ & V = \left\{ \frac{-24}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-2x+6)& = & 6 \color{red}{+} (9+x) \\\Leftrightarrow & -12x+36& = &6+9+x \\\Leftrightarrow & -12x \color{red}{+36} & = &15 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & -12x-x& = &15-36 \\\Leftrightarrow & -13x& = &-21 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-21}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{21}{13} & & \\ & V = \left\{ \frac{21}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (x-3)& = & 13 \color{red}{+} (14+4x) \\\Leftrightarrow & 3x-9& = &13+14+4x \\\Leftrightarrow & 3x \color{red}{-9} & = &27 \color{red}{+4x} \\\Leftrightarrow & 3x \color{red}{-9} \color{blue}{+9} \color{blue}{-4x} & = &27 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+9} \\\Leftrightarrow & 3x-4x& = &27+9 \\\Leftrightarrow & -x& = &36 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{36}{ \color{red}{-1} } \\\Leftrightarrow & x = -36 & & \\ & V = \left\{ -36 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (3x-1)& = & -7 \color{red}{+} (10-5x) \\\Leftrightarrow & 18x-6& = &-7+10-5x \\\Leftrightarrow & 18x \color{red}{-6} & = &3 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &3 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & 18x+5x& = &3+6 \\\Leftrightarrow & 23x& = &9 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{9}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{9}{23} & & \\ & V = \left\{ \frac{9}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-4x-1)& = & -6 \color{red}{-} (14+3x) \\\Leftrightarrow & -8x-2& = &-6-14-3x \\\Leftrightarrow & -8x \color{red}{-2} & = &-20 \color{red}{-3x} \\\Leftrightarrow & -8x \color{red}{-2} \color{blue}{+2} \color{blue}{+3x} & = &-20 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+2} \\\Leftrightarrow & -8x+3x& = &-20+2 \\\Leftrightarrow & -5x& = &-18 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-18}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{18}{5} & & \\ & V = \left\{ \frac{18}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-3x+1)& = & -1 \color{red}{+} (-2-2x) \\\Leftrightarrow & -15x+5& = &-1-2-2x \\\Leftrightarrow & -15x \color{red}{+5} & = &-3 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+5} \color{blue}{-5} \color{blue}{+2x} & = &-3 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-5} \\\Leftrightarrow & -15x+2x& = &-3-5 \\\Leftrightarrow & -13x& = &-8 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-8}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{8}{13} & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (5x+5)& = & -1 \color{red}{-} (-14+x) \\\Leftrightarrow & 30x+30& = &-1+14-x \\\Leftrightarrow & 30x \color{red}{+30} & = &13 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & 30x+x& = &13-30 \\\Leftrightarrow & 31x& = &-17 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-17}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-17}{31} & & \\ & V = \left\{ \frac{-17}{31} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (3x-5)& = & -6 \color{red}{+} (7-2x) \\\Leftrightarrow & 15x-25& = &-6+7-2x \\\Leftrightarrow & 15x \color{red}{-25} & = &1 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-25} \color{blue}{+25} \color{blue}{+2x} & = &1 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+25} \\\Leftrightarrow & 15x+2x& = &1+25 \\\Leftrightarrow & 17x& = &26 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{26}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{26}{17} & & \\ & V = \left\{ \frac{26}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-5x+6)& = & -7 \color{red}{-} (-10+x) \\\Leftrightarrow & -30x+36& = &-7+10-x \\\Leftrightarrow & -30x \color{red}{+36} & = &3 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & -30x+x& = &3-36 \\\Leftrightarrow & -29x& = &-33 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-33}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{33}{29} & & \\ & V = \left\{ \frac{33}{29} \right\} & \\\end{align}\)