Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-6x-2)& = & -5 \color{red}{+} (15+x) \\\Leftrightarrow & -30x-10& = &-5+15+x \\\Leftrightarrow & -30x \color{red}{-10} & = &10 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & -30x-x& = &10+10 \\\Leftrightarrow & -31x& = &20 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{20}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-20}{31} & & \\ & V = \left\{ \frac{-20}{31} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-3x+6)& = & 1 \color{red}{-} (-10+x) \\\Leftrightarrow & -12x+24& = &1+10-x \\\Leftrightarrow & -12x \color{red}{+24} & = &11 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -12x+x& = &11-24 \\\Leftrightarrow & -11x& = &-13 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-13}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{13}{11} & & \\ & V = \left\{ \frac{13}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (6x+7)& = & 3 \color{red}{+} (-2+x) \\\Leftrightarrow & 12x+14& = &3-2+x \\\Leftrightarrow & 12x \color{red}{+14} & = &1 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+14} \color{blue}{-14} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-14} \\\Leftrightarrow & 12x-x& = &1-14 \\\Leftrightarrow & 11x& = &-13 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-13}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-13}{11} & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-5x-6)& = & -8 \color{red}{+} (-14+x) \\\Leftrightarrow & -20x-24& = &-8-14+x \\\Leftrightarrow & -20x \color{red}{-24} & = &-22 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-22 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -20x-x& = &-22+24 \\\Leftrightarrow & -21x& = &2 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{2}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-2}{21} & & \\ & V = \left\{ \frac{-2}{21} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (x-1)& = & -5 \color{red}{+} (-15+x) \\\Leftrightarrow & 2x-2& = &-5-15+x \\\Leftrightarrow & 2x \color{red}{-2} & = &-20 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & 2x-x& = &-20+2 \\\Leftrightarrow & x& = &-18 \\ & V = \left\{ -18 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-5x+5)& = & -1 \color{red}{+} (-9+x) \\\Leftrightarrow & -20x+20& = &-1-9+x \\\Leftrightarrow & -20x \color{red}{+20} & = &-10 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & -20x-x& = &-10-20 \\\Leftrightarrow & -21x& = &-30 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-30}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{10}{7} & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (x+4)& = & 12 \color{red}{+} (-14-5x) \\\Leftrightarrow & 6x+24& = &12-14-5x \\\Leftrightarrow & 6x \color{red}{+24} & = &-2 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+24} \color{blue}{-24} \color{blue}{+5x} & = &-2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-24} \\\Leftrightarrow & 6x+5x& = &-2-24 \\\Leftrightarrow & 11x& = &-26 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-26}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-26}{11} & & \\ & V = \left\{ \frac{-26}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-4x+3)& = & -6 \color{red}{+} (-8+x) \\\Leftrightarrow & -24x+18& = &-6-8+x \\\Leftrightarrow & -24x \color{red}{+18} & = &-14 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & -24x-x& = &-14-18 \\\Leftrightarrow & -25x& = &-32 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-32}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{32}{25} & & \\ & V = \left\{ \frac{32}{25} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-5x+7)& = & -4 \color{red}{-} (-15+x) \\\Leftrightarrow & -30x+42& = &-4+15-x \\\Leftrightarrow & -30x \color{red}{+42} & = &11 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & -30x+x& = &11-42 \\\Leftrightarrow & -29x& = &-31 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-31}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{31}{29} & & \\ & V = \left\{ \frac{31}{29} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-5x+7)& = & 13 \color{red}{-} (9+x) \\\Leftrightarrow & -10x+14& = &13-9-x \\\Leftrightarrow & -10x \color{red}{+14} & = &4 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{+14} \color{blue}{-14} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{-14} \\\Leftrightarrow & -10x+x& = &4-14 \\\Leftrightarrow & -9x& = &-10 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-10}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{10}{9} & & \\ & V = \left\{ \frac{10}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (5x+5)& = & -15 \color{red}{-} (-7+3x) \\\Leftrightarrow & 10x+10& = &-15+7-3x \\\Leftrightarrow & 10x \color{red}{+10} & = &-8 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+10} \color{blue}{-10} \color{blue}{+3x} & = &-8 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-10} \\\Leftrightarrow & 10x+3x& = &-8-10 \\\Leftrightarrow & 13x& = &-18 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-18}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-18}{13} & & \\ & V = \left\{ \frac{-18}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-4x-2)& = & 1 \color{red}{+} (-6+x) \\\Leftrightarrow & -20x-10& = &1-6+x \\\Leftrightarrow & -20x \color{red}{-10} & = &-5 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & -20x-x& = &-5+10 \\\Leftrightarrow & -21x& = &5 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{5}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-5}{21} & & \\ & V = \left\{ \frac{-5}{21} \right\} & \\\end{align}\)