Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-4x-5)& = & 1 \color{red}{+} (1+x) \\\Leftrightarrow & -20x-25& = &1+1+x \\\Leftrightarrow & -20x \color{red}{-25} & = &2 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-25} \color{blue}{+25} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{+25} \\\Leftrightarrow & -20x-x& = &2+25 \\\Leftrightarrow & -21x& = &27 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{27}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-9}{7} & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-6x-2)& = & -14 \color{red}{-} (7+x) \\\Leftrightarrow & -12x-4& = &-14-7-x \\\Leftrightarrow & -12x \color{red}{-4} & = &-21 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-21 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -12x+x& = &-21+4 \\\Leftrightarrow & -11x& = &-17 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-17}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{17}{11} & & \\ & V = \left\{ \frac{17}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (6x-5)& = & -9 \color{red}{+} (3+x) \\\Leftrightarrow & 18x-15& = &-9+3+x \\\Leftrightarrow & 18x \color{red}{-15} & = &-6 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & 18x-x& = &-6+15 \\\Leftrightarrow & 17x& = &9 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{9}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{9}{17} & & \\ & V = \left\{ \frac{9}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (5x-5)& = & -1 \color{red}{+} (4+x) \\\Leftrightarrow & 30x-30& = &-1+4+x \\\Leftrightarrow & 30x \color{red}{-30} & = &3 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 30x-x& = &3+30 \\\Leftrightarrow & 29x& = &33 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{33}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{33}{29} & & \\ & V = \left\{ \frac{33}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-5x-4)& = & -1 \color{red}{+} (11+x) \\\Leftrightarrow & -15x-12& = &-1+11+x \\\Leftrightarrow & -15x \color{red}{-12} & = &10 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -15x-x& = &10+12 \\\Leftrightarrow & -16x& = &22 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{22}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{-11}{8} & & \\ & V = \left\{ \frac{-11}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (x+4)& = & -3 \color{red}{+} (9-2x) \\\Leftrightarrow & 5x+20& = &-3+9-2x \\\Leftrightarrow & 5x \color{red}{+20} & = &6 \color{red}{-2x} \\\Leftrightarrow & 5x \color{red}{+20} \color{blue}{-20} \color{blue}{+2x} & = &6 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-20} \\\Leftrightarrow & 5x+2x& = &6-20 \\\Leftrightarrow & 7x& = &-14 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-14}{ \color{red}{7} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (2x+1)& = & -6 \color{red}{-} (8+x) \\\Leftrightarrow & 12x+6& = &-6-8-x \\\Leftrightarrow & 12x \color{red}{+6} & = &-14 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 12x+x& = &-14-6 \\\Leftrightarrow & 13x& = &-20 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-20}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-20}{13} & & \\ & V = \left\{ \frac{-20}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-4x+1)& = & 6 \color{red}{-} (7+x) \\\Leftrightarrow & -16x+4& = &6-7-x \\\Leftrightarrow & -16x \color{red}{+4} & = &-1 \color{red}{-x} \\\Leftrightarrow & -16x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -16x+x& = &-1-4 \\\Leftrightarrow & -15x& = &-5 \\\Leftrightarrow & \frac{-15x}{ \color{red}{-15} }& = &\frac{-5}{ \color{red}{-15} } \\\Leftrightarrow & x = \frac{1}{3} & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-4x+3)& = & -8 \color{red}{-} (9+x) \\\Leftrightarrow & -24x+18& = &-8-9-x \\\Leftrightarrow & -24x \color{red}{+18} & = &-17 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -24x+x& = &-17-18 \\\Leftrightarrow & -23x& = &-35 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-35}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{35}{23} & & \\ & V = \left\{ \frac{35}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (2x-5)& = & 14 \color{red}{+} (-12+3x) \\\Leftrightarrow & 4x-10& = &14-12+3x \\\Leftrightarrow & 4x \color{red}{-10} & = &2 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & 4x-3x& = &2+10 \\\Leftrightarrow & x& = &12 \\ & V = \left\{ 12 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (x+1)& = & 1 \color{red}{+} (-8+3x) \\\Leftrightarrow & 2x+2& = &1-8+3x \\\Leftrightarrow & 2x \color{red}{+2} & = &-7 \color{red}{+3x} \\\Leftrightarrow & 2x \color{red}{+2} \color{blue}{-2} \color{blue}{-3x} & = &-7 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-2} \\\Leftrightarrow & 2x-3x& = &-7-2 \\\Leftrightarrow & -x& = &-9 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-9}{ \color{red}{-1} } \\\Leftrightarrow & x = 9 & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-2x+7)& = & 1 \color{red}{+} (-3+x) \\\Leftrightarrow & -8x+28& = &1-3+x \\\Leftrightarrow & -8x \color{red}{+28} & = &-2 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & -8x-x& = &-2-28 \\\Leftrightarrow & -9x& = &-30 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-30}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{10}{3} & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)