Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-2x-6)& = & -15 \color{red}{-} (-9+x) \\\Leftrightarrow & -10x-30& = &-15+9-x \\\Leftrightarrow & -10x \color{red}{-30} & = &-6 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & -10x+x& = &-6+30 \\\Leftrightarrow & -9x& = &24 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{24}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-8}{3} & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-5x-4)& = & -15 \color{red}{+} (-1+4x) \\\Leftrightarrow & -15x-12& = &-15-1+4x \\\Leftrightarrow & -15x \color{red}{-12} & = &-16 \color{red}{+4x} \\\Leftrightarrow & -15x \color{red}{-12} \color{blue}{+12} \color{blue}{-4x} & = &-16 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+12} \\\Leftrightarrow & -15x-4x& = &-16+12 \\\Leftrightarrow & -19x& = &-4 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-4}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{4}{19} & & \\ & V = \left\{ \frac{4}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-2x-3)& = & -3 \color{red}{-} (5+x) \\\Leftrightarrow & -4x-6& = &-3-5-x \\\Leftrightarrow & -4x \color{red}{-6} & = &-8 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -4x+x& = &-8+6 \\\Leftrightarrow & -3x& = &-2 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-2}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{2}{3} & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (x-2)& = & -4 \color{red}{-} (8+x) \\\Leftrightarrow & 4x-8& = &-4-8-x \\\Leftrightarrow & 4x \color{red}{-8} & = &-12 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 4x+x& = &-12+8 \\\Leftrightarrow & 5x& = &-4 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-4}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-4}{5} & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (3x-7)& = & 12 \color{red}{-} (-14+x) \\\Leftrightarrow & 18x-42& = &12+14-x \\\Leftrightarrow & 18x \color{red}{-42} & = &26 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &26 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & 18x+x& = &26+42 \\\Leftrightarrow & 19x& = &68 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{68}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{68}{19} & & \\ & V = \left\{ \frac{68}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-5x+6)& = & -10 \color{red}{-} (4-3x) \\\Leftrightarrow & -10x+12& = &-10-4+3x \\\Leftrightarrow & -10x \color{red}{+12} & = &-14 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+12} \color{blue}{-12} \color{blue}{-3x} & = &-14 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-12} \\\Leftrightarrow & -10x-3x& = &-14-12 \\\Leftrightarrow & -13x& = &-26 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-26}{ \color{red}{-13} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-3x-4)& = & -14 \color{red}{+} (-9+x) \\\Leftrightarrow & -18x-24& = &-14-9+x \\\Leftrightarrow & -18x \color{red}{-24} & = &-23 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-23 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -18x-x& = &-23+24 \\\Leftrightarrow & -19x& = &1 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{1}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-1}{19} & & \\ & V = \left\{ \frac{-1}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-x-3)& = & 8 \color{red}{+} (14+4x) \\\Leftrightarrow & -5x-15& = &8+14+4x \\\Leftrightarrow & -5x \color{red}{-15} & = &22 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{-15} \color{blue}{+15} \color{blue}{-4x} & = &22 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+15} \\\Leftrightarrow & -5x-4x& = &22+15 \\\Leftrightarrow & -9x& = &37 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{37}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-37}{9} & & \\ & V = \left\{ \frac{-37}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-5x-5)& = & -8 \color{red}{-} (-6+x) \\\Leftrightarrow & -30x-30& = &-8+6-x \\\Leftrightarrow & -30x \color{red}{-30} & = &-2 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & -30x+x& = &-2+30 \\\Leftrightarrow & -29x& = &28 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{28}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-28}{29} & & \\ & V = \left\{ \frac{-28}{29} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (6x+4)& = & -15 \color{red}{-} (-2+x) \\\Leftrightarrow & 18x+12& = &-15+2-x \\\Leftrightarrow & 18x \color{red}{+12} & = &-13 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 18x+x& = &-13-12 \\\Leftrightarrow & 19x& = &-25 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-25}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-25}{19} & & \\ & V = \left\{ \frac{-25}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (3x+3)& = & -1 \color{red}{+} (-1+x) \\\Leftrightarrow & 15x+15& = &-1-1+x \\\Leftrightarrow & 15x \color{red}{+15} & = &-2 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & 15x-x& = &-2-15 \\\Leftrightarrow & 14x& = &-17 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{-17}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{-17}{14} & & \\ & V = \left\{ \frac{-17}{14} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (4x-3)& = & -6 \color{red}{-} (-15+x) \\\Leftrightarrow & 8x-6& = &-6+15-x \\\Leftrightarrow & 8x \color{red}{-6} & = &9 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 8x+x& = &9+6 \\\Leftrightarrow & 9x& = &15 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{15}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{5}{3} & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)