Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (6x-7)& = & -14 \color{red}{-} (6-5x) \\\Leftrightarrow & 18x-21& = &-14-6+5x \\\Leftrightarrow & 18x \color{red}{-21} & = &-20 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-21} \color{blue}{+21} \color{blue}{-5x} & = &-20 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+21} \\\Leftrightarrow & 18x-5x& = &-20+21 \\\Leftrightarrow & 13x& = &1 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{1}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{1}{13} & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-6x-2)& = & -15 \color{red}{+} (6+x) \\\Leftrightarrow & -36x-12& = &-15+6+x \\\Leftrightarrow & -36x \color{red}{-12} & = &-9 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -36x-x& = &-9+12 \\\Leftrightarrow & -37x& = &3 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{3}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{-3}{37} & & \\ & V = \left\{ \frac{-3}{37} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-3x+6)& = & -14 \color{red}{-} (15+2x) \\\Leftrightarrow & -15x+30& = &-14-15-2x \\\Leftrightarrow & -15x \color{red}{+30} & = &-29 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+30} \color{blue}{-30} \color{blue}{+2x} & = &-29 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-30} \\\Leftrightarrow & -15x+2x& = &-29-30 \\\Leftrightarrow & -13x& = &-59 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-59}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{59}{13} & & \\ & V = \left\{ \frac{59}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (4x-6)& = & -11 \color{red}{+} (-1+x) \\\Leftrightarrow & 12x-18& = &-11-1+x \\\Leftrightarrow & 12x \color{red}{-18} & = &-12 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 12x-x& = &-12+18 \\\Leftrightarrow & 11x& = &6 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{6}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{6}{11} & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (3x-7)& = & -13 \color{red}{-} (-12+x) \\\Leftrightarrow & 12x-28& = &-13+12-x \\\Leftrightarrow & 12x \color{red}{-28} & = &-1 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & 12x+x& = &-1+28 \\\Leftrightarrow & 13x& = &27 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{27}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{27}{13} & & \\ & V = \left\{ \frac{27}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (5x-2)& = & -3 \color{red}{+} (9-2x) \\\Leftrightarrow & 15x-6& = &-3+9-2x \\\Leftrightarrow & 15x \color{red}{-6} & = &6 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-6} \color{blue}{+6} \color{blue}{+2x} & = &6 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+6} \\\Leftrightarrow & 15x+2x& = &6+6 \\\Leftrightarrow & 17x& = &12 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{12}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{12}{17} & & \\ & V = \left\{ \frac{12}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-4x+2)& = & -14 \color{red}{-} (-3+x) \\\Leftrightarrow & -8x+4& = &-14+3-x \\\Leftrightarrow & -8x \color{red}{+4} & = &-11 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -8x+x& = &-11-4 \\\Leftrightarrow & -7x& = &-15 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-15}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{15}{7} & & \\ & V = \left\{ \frac{15}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (4x+5)& = & -4 \color{red}{-} (-15+x) \\\Leftrightarrow & 8x+10& = &-4+15-x \\\Leftrightarrow & 8x \color{red}{+10} & = &11 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 8x+x& = &11-10 \\\Leftrightarrow & 9x& = &1 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{1}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{1}{9} & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-6x-3)& = & 11 \color{red}{+} (-7+x) \\\Leftrightarrow & -12x-6& = &11-7+x \\\Leftrightarrow & -12x \color{red}{-6} & = &4 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -12x-x& = &4+6 \\\Leftrightarrow & -13x& = &10 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{10}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-10}{13} & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-6x+7)& = & -13 \color{red}{+} (-11+x) \\\Leftrightarrow & -18x+21& = &-13-11+x \\\Leftrightarrow & -18x \color{red}{+21} & = &-24 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+21} \color{blue}{-21} \color{blue}{-x} & = &-24 \color{red}{+x} \color{blue}{-x} \color{blue}{-21} \\\Leftrightarrow & -18x-x& = &-24-21 \\\Leftrightarrow & -19x& = &-45 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-45}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{45}{19} & & \\ & V = \left\{ \frac{45}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (4x-5)& = & 11 \color{red}{+} (4+x) \\\Leftrightarrow & 16x-20& = &11+4+x \\\Leftrightarrow & 16x \color{red}{-20} & = &15 \color{red}{+x} \\\Leftrightarrow & 16x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 16x-x& = &15+20 \\\Leftrightarrow & 15x& = &35 \\\Leftrightarrow & \frac{15x}{ \color{red}{15} }& = &\frac{35}{ \color{red}{15} } \\\Leftrightarrow & x = \frac{7}{3} & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-2x-6)& = & 6 \color{red}{-} (-6-5x) \\\Leftrightarrow & -8x-24& = &6+6+5x \\\Leftrightarrow & -8x \color{red}{-24} & = &12 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{-24} \color{blue}{+24} \color{blue}{-5x} & = &12 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+24} \\\Leftrightarrow & -8x-5x& = &12+24 \\\Leftrightarrow & -13x& = &36 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{36}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-36}{13} & & \\ & V = \left\{ \frac{-36}{13} \right\} & \\\end{align}\)