Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (6x+6)& = & 9 \color{red}{-} (-7+x) \\\Leftrightarrow & 12x+12& = &9+7-x \\\Leftrightarrow & 12x \color{red}{+12} & = &16 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 12x+x& = &16-12 \\\Leftrightarrow & 13x& = &4 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{4}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{4}{13} & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (3x-3)& = & 4 \color{red}{+} (7+x) \\\Leftrightarrow & 12x-12& = &4+7+x \\\Leftrightarrow & 12x \color{red}{-12} & = &11 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 12x-x& = &11+12 \\\Leftrightarrow & 11x& = &23 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{23}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{23}{11} & & \\ & V = \left\{ \frac{23}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (x+7)& = & 5 \color{red}{+} (11+x) \\\Leftrightarrow & 2x+14& = &5+11+x \\\Leftrightarrow & 2x \color{red}{+14} & = &16 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{+14} \color{blue}{-14} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{-14} \\\Leftrightarrow & 2x-x& = &16-14 \\\Leftrightarrow & x& = &2 \\ & V = \left\{ 2 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-4x-6)& = & -8 \color{red}{+} (10+x) \\\Leftrightarrow & -8x-12& = &-8+10+x \\\Leftrightarrow & -8x \color{red}{-12} & = &2 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -8x-x& = &2+12 \\\Leftrightarrow & -9x& = &14 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{14}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-14}{9} & & \\ & V = \left\{ \frac{-14}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (6x-2)& = & 12 \color{red}{+} (2-5x) \\\Leftrightarrow & 36x-12& = &12+2-5x \\\Leftrightarrow & 36x \color{red}{-12} & = &14 \color{red}{-5x} \\\Leftrightarrow & 36x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &14 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & 36x+5x& = &14+12 \\\Leftrightarrow & 41x& = &26 \\\Leftrightarrow & \frac{41x}{ \color{red}{41} }& = &\frac{26}{ \color{red}{41} } \\\Leftrightarrow & x = \frac{26}{41} & & \\ & V = \left\{ \frac{26}{41} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (5x-6)& = & -10 \color{red}{+} (5-3x) \\\Leftrightarrow & 25x-30& = &-10+5-3x \\\Leftrightarrow & 25x \color{red}{-30} & = &-5 \color{red}{-3x} \\\Leftrightarrow & 25x \color{red}{-30} \color{blue}{+30} \color{blue}{+3x} & = &-5 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+30} \\\Leftrightarrow & 25x+3x& = &-5+30 \\\Leftrightarrow & 28x& = &25 \\\Leftrightarrow & \frac{28x}{ \color{red}{28} }& = &\frac{25}{ \color{red}{28} } \\\Leftrightarrow & x = \frac{25}{28} & & \\ & V = \left\{ \frac{25}{28} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-x+7)& = & -6 \color{red}{-} (12+4x) \\\Leftrightarrow & -3x+21& = &-6-12-4x \\\Leftrightarrow & -3x \color{red}{+21} & = &-18 \color{red}{-4x} \\\Leftrightarrow & -3x \color{red}{+21} \color{blue}{-21} \color{blue}{+4x} & = &-18 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-21} \\\Leftrightarrow & -3x+4x& = &-18-21 \\\Leftrightarrow & x& = &-39 \\ & V = \left\{ -39 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (x+2)& = & -3 \color{red}{+} (-12+x) \\\Leftrightarrow & 2x+4& = &-3-12+x \\\Leftrightarrow & 2x \color{red}{+4} & = &-15 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 2x-x& = &-15-4 \\\Leftrightarrow & x& = &-19 \\ & V = \left\{ -19 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (2x-3)& = & -11 \color{red}{+} (-10+x) \\\Leftrightarrow & 10x-15& = &-11-10+x \\\Leftrightarrow & 10x \color{red}{-15} & = &-21 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &-21 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & 10x-x& = &-21+15 \\\Leftrightarrow & 9x& = &-6 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-6}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-2}{3} & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-2x-2)& = & -4 \color{red}{-} (15+x) \\\Leftrightarrow & -12x-12& = &-4-15-x \\\Leftrightarrow & -12x \color{red}{-12} & = &-19 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -12x+x& = &-19+12 \\\Leftrightarrow & -11x& = &-7 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-7}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{7}{11} & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-3x-3)& = & -9 \color{red}{+} (-5+x) \\\Leftrightarrow & -6x-6& = &-9-5+x \\\Leftrightarrow & -6x \color{red}{-6} & = &-14 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -6x-x& = &-14+6 \\\Leftrightarrow & -7x& = &-8 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-8}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{8}{7} & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-5x+2)& = & 6 \color{red}{-} (1+x) \\\Leftrightarrow & -30x+12& = &6-1-x \\\Leftrightarrow & -30x \color{red}{+12} & = &5 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -30x+x& = &5-12 \\\Leftrightarrow & -29x& = &-7 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-7}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{7}{29} & & \\ & V = \left\{ \frac{7}{29} \right\} & \\\end{align}\)