Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-4x+4)& = & -10 \color{red}{-} (3+x) \\\Leftrightarrow & -12x+12& = &-10-3-x \\\Leftrightarrow & -12x \color{red}{+12} & = &-13 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -12x+x& = &-13-12 \\\Leftrightarrow & -11x& = &-25 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-25}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{25}{11} & & \\ & V = \left\{ \frac{25}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (2x-1)& = & 4 \color{red}{-} (-12+x) \\\Leftrightarrow & 8x-4& = &4+12-x \\\Leftrightarrow & 8x \color{red}{-4} & = &16 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 8x+x& = &16+4 \\\Leftrightarrow & 9x& = &20 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{20}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{20}{9} & & \\ & V = \left\{ \frac{20}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (3x+6)& = & -12 \color{red}{-} (-14+x) \\\Leftrightarrow & 18x+36& = &-12+14-x \\\Leftrightarrow & 18x \color{red}{+36} & = &2 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & 18x+x& = &2-36 \\\Leftrightarrow & 19x& = &-34 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-34}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-34}{19} & & \\ & V = \left\{ \frac{-34}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (5x-4)& = & -12 \color{red}{+} (-9+x) \\\Leftrightarrow & 20x-16& = &-12-9+x \\\Leftrightarrow & 20x \color{red}{-16} & = &-21 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &-21 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & 20x-x& = &-21+16 \\\Leftrightarrow & 19x& = &-5 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-5}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-5}{19} & & \\ & V = \left\{ \frac{-5}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-3x-7)& = & -9 \color{red}{+} (-9+x) \\\Leftrightarrow & -18x-42& = &-9-9+x \\\Leftrightarrow & -18x \color{red}{-42} & = &-18 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &-18 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & -18x-x& = &-18+42 \\\Leftrightarrow & -19x& = &24 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{24}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-24}{19} & & \\ & V = \left\{ \frac{-24}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-2x+5)& = & 4 \color{red}{-} (6+x) \\\Leftrightarrow & -10x+25& = &4-6-x \\\Leftrightarrow & -10x \color{red}{+25} & = &-2 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{+25} \color{blue}{-25} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{-25} \\\Leftrightarrow & -10x+x& = &-2-25 \\\Leftrightarrow & -9x& = &-27 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-27}{ \color{red}{-9} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-4x+3)& = & -12 \color{red}{+} (-8+x) \\\Leftrightarrow & -12x+9& = &-12-8+x \\\Leftrightarrow & -12x \color{red}{+9} & = &-20 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+9} \color{blue}{-9} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{-9} \\\Leftrightarrow & -12x-x& = &-20-9 \\\Leftrightarrow & -13x& = &-29 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-29}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{29}{13} & & \\ & V = \left\{ \frac{29}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-5x+3)& = & -6 \color{red}{-} (-7+x) \\\Leftrightarrow & -30x+18& = &-6+7-x \\\Leftrightarrow & -30x \color{red}{+18} & = &1 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -30x+x& = &1-18 \\\Leftrightarrow & -29x& = &-17 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-17}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{17}{29} & & \\ & V = \left\{ \frac{17}{29} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-6x+4)& = & 8 \color{red}{+} (-8+x) \\\Leftrightarrow & -30x+20& = &8-8+x \\\Leftrightarrow & -30x \color{red}{+20} & = &0 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & -30x-x& = &0-20 \\\Leftrightarrow & -31x& = &-20 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-20}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{20}{31} & & \\ & V = \left\{ \frac{20}{31} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (3x-4)& = & 15 \color{red}{+} (-15-5x) \\\Leftrightarrow & 6x-8& = &15-15-5x \\\Leftrightarrow & 6x \color{red}{-8} & = &0 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-8} \color{blue}{+8} \color{blue}{+5x} & = &0 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+8} \\\Leftrightarrow & 6x+5x& = &0+8 \\\Leftrightarrow & 11x& = &8 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{8}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{8}{11} & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (6x+6)& = & 4 \color{red}{-} (-3+x) \\\Leftrightarrow & 24x+24& = &4+3-x \\\Leftrightarrow & 24x \color{red}{+24} & = &7 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 24x+x& = &7-24 \\\Leftrightarrow & 25x& = &-17 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-17}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-17}{25} & & \\ & V = \left\{ \frac{-17}{25} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-6x+1)& = & 5 \color{red}{-} (-14+x) \\\Leftrightarrow & -24x+4& = &5+14-x \\\Leftrightarrow & -24x \color{red}{+4} & = &19 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &19 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -24x+x& = &19-4 \\\Leftrightarrow & -23x& = &15 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{15}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-15}{23} & & \\ & V = \left\{ \frac{-15}{23} \right\} & \\\end{align}\)