Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-2x+7)& = & -8 \color{red}{-} (-9-3x) \\\Leftrightarrow & -10x+35& = &-8+9+3x \\\Leftrightarrow & -10x \color{red}{+35} & = &1 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+35} \color{blue}{-35} \color{blue}{-3x} & = &1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-35} \\\Leftrightarrow & -10x-3x& = &1-35 \\\Leftrightarrow & -13x& = &-34 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-34}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{34}{13} & & \\ & V = \left\{ \frac{34}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (x-4)& = & -14 \color{red}{+} (-11+4x) \\\Leftrightarrow & 3x-12& = &-14-11+4x \\\Leftrightarrow & 3x \color{red}{-12} & = &-25 \color{red}{+4x} \\\Leftrightarrow & 3x \color{red}{-12} \color{blue}{+12} \color{blue}{-4x} & = &-25 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+12} \\\Leftrightarrow & 3x-4x& = &-25+12 \\\Leftrightarrow & -x& = &-13 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-13}{ \color{red}{-1} } \\\Leftrightarrow & x = 13 & & \\ & V = \left\{ 13 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (6x-7)& = & 3 \color{red}{+} (13+x) \\\Leftrightarrow & 12x-14& = &3+13+x \\\Leftrightarrow & 12x \color{red}{-14} & = &16 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & 12x-x& = &16+14 \\\Leftrightarrow & 11x& = &30 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{30}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{30}{11} & & \\ & V = \left\{ \frac{30}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (6x+3)& = & 10 \color{red}{+} (9+x) \\\Leftrightarrow & 30x+15& = &10+9+x \\\Leftrightarrow & 30x \color{red}{+15} & = &19 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & 30x-x& = &19-15 \\\Leftrightarrow & 29x& = &4 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{4}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{4}{29} & & \\ & V = \left\{ \frac{4}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-x-5)& = & 9 \color{red}{-} (3-2x) \\\Leftrightarrow & -3x-15& = &9-3+2x \\\Leftrightarrow & -3x \color{red}{-15} & = &6 \color{red}{+2x} \\\Leftrightarrow & -3x \color{red}{-15} \color{blue}{+15} \color{blue}{-2x} & = &6 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+15} \\\Leftrightarrow & -3x-2x& = &6+15 \\\Leftrightarrow & -5x& = &21 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{21}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-21}{5} & & \\ & V = \left\{ \frac{-21}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (x+2)& = & -14 \color{red}{-} (14+x) \\\Leftrightarrow & 3x+6& = &-14-14-x \\\Leftrightarrow & 3x \color{red}{+6} & = &-28 \color{red}{-x} \\\Leftrightarrow & 3x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-28 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 3x+x& = &-28-6 \\\Leftrightarrow & 4x& = &-34 \\\Leftrightarrow & \frac{4x}{ \color{red}{4} }& = &\frac{-34}{ \color{red}{4} } \\\Leftrightarrow & x = \frac{-17}{2} & & \\ & V = \left\{ \frac{-17}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-4x+6)& = & -11 \color{red}{+} (14+x) \\\Leftrightarrow & -12x+18& = &-11+14+x \\\Leftrightarrow & -12x \color{red}{+18} & = &3 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & -12x-x& = &3-18 \\\Leftrightarrow & -13x& = &-15 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-15}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{15}{13} & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-6x+5)& = & -12 \color{red}{+} (-10+x) \\\Leftrightarrow & -24x+20& = &-12-10+x \\\Leftrightarrow & -24x \color{red}{+20} & = &-22 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &-22 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & -24x-x& = &-22-20 \\\Leftrightarrow & -25x& = &-42 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-42}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{42}{25} & & \\ & V = \left\{ \frac{42}{25} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (x-2)& = & 14 \color{red}{+} (3-4x) \\\Leftrightarrow & 5x-10& = &14+3-4x \\\Leftrightarrow & 5x \color{red}{-10} & = &17 \color{red}{-4x} \\\Leftrightarrow & 5x \color{red}{-10} \color{blue}{+10} \color{blue}{+4x} & = &17 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+10} \\\Leftrightarrow & 5x+4x& = &17+10 \\\Leftrightarrow & 9x& = &27 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{27}{ \color{red}{9} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (6x-4)& = & -15 \color{red}{-} (-5+x) \\\Leftrightarrow & 30x-20& = &-15+5-x \\\Leftrightarrow & 30x \color{red}{-20} & = &-10 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 30x+x& = &-10+20 \\\Leftrightarrow & 31x& = &10 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{10}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{10}{31} & & \\ & V = \left\{ \frac{10}{31} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (6x-2)& = & 6 \color{red}{+} (11+x) \\\Leftrightarrow & 18x-6& = &6+11+x \\\Leftrightarrow & 18x \color{red}{-6} & = &17 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &17 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 18x-x& = &17+6 \\\Leftrightarrow & 17x& = &23 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{23}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{23}{17} & & \\ & V = \left\{ \frac{23}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-4x+6)& = & 10 \color{red}{-} (-12+x) \\\Leftrightarrow & -20x+30& = &10+12-x \\\Leftrightarrow & -20x \color{red}{+30} & = &22 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &22 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & -20x+x& = &22-30 \\\Leftrightarrow & -19x& = &-8 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-8}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{8}{19} & & \\ & V = \left\{ \frac{8}{19} \right\} & \\\end{align}\)