Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-5x-2)& = & -1 \color{red}{+} (-6-3x) \\\Leftrightarrow & -10x-4& = &-1-6-3x \\\Leftrightarrow & -10x \color{red}{-4} & = &-7 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{-4} \color{blue}{+4} \color{blue}{+3x} & = &-7 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+4} \\\Leftrightarrow & -10x+3x& = &-7+4 \\\Leftrightarrow & -7x& = &-3 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-3}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{3}{7} & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (5x+5)& = & -1 \color{red}{+} (3+x) \\\Leftrightarrow & 20x+20& = &-1+3+x \\\Leftrightarrow & 20x \color{red}{+20} & = &2 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 20x-x& = &2-20 \\\Leftrightarrow & 19x& = &-18 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-18}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-18}{19} & & \\ & V = \left\{ \frac{-18}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-6x-7)& = & 8 \color{red}{-} (-3-5x) \\\Leftrightarrow & -18x-21& = &8+3+5x \\\Leftrightarrow & -18x \color{red}{-21} & = &11 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{-21} \color{blue}{+21} \color{blue}{-5x} & = &11 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+21} \\\Leftrightarrow & -18x-5x& = &11+21 \\\Leftrightarrow & -23x& = &32 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{32}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-32}{23} & & \\ & V = \left\{ \frac{-32}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (6x+2)& = & -13 \color{red}{+} (-13+x) \\\Leftrightarrow & 12x+4& = &-13-13+x \\\Leftrightarrow & 12x \color{red}{+4} & = &-26 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &-26 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 12x-x& = &-26-4 \\\Leftrightarrow & 11x& = &-30 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-30}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-30}{11} & & \\ & V = \left\{ \frac{-30}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-4x-2)& = & 14 \color{red}{-} (4+x) \\\Leftrightarrow & -24x-12& = &14-4-x \\\Leftrightarrow & -24x \color{red}{-12} & = &10 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -24x+x& = &10+12 \\\Leftrightarrow & -23x& = &22 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{22}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-22}{23} & & \\ & V = \left\{ \frac{-22}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-5x-7)& = & 14 \color{red}{+} (-3-3x) \\\Leftrightarrow & -10x-14& = &14-3-3x \\\Leftrightarrow & -10x \color{red}{-14} & = &11 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{-14} \color{blue}{+14} \color{blue}{+3x} & = &11 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+14} \\\Leftrightarrow & -10x+3x& = &11+14 \\\Leftrightarrow & -7x& = &25 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{25}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-25}{7} & & \\ & V = \left\{ \frac{-25}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-3x-6)& = & -13 \color{red}{+} (-14-5x) \\\Leftrightarrow & -18x-36& = &-13-14-5x \\\Leftrightarrow & -18x \color{red}{-36} & = &-27 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-36} \color{blue}{+36} \color{blue}{+5x} & = &-27 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+36} \\\Leftrightarrow & -18x+5x& = &-27+36 \\\Leftrightarrow & -13x& = &9 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{9}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-9}{13} & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-6x+7)& = & -11 \color{red}{+} (-4+x) \\\Leftrightarrow & -24x+28& = &-11-4+x \\\Leftrightarrow & -24x \color{red}{+28} & = &-15 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & -24x-x& = &-15-28 \\\Leftrightarrow & -25x& = &-43 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-43}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{43}{25} & & \\ & V = \left\{ \frac{43}{25} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-2x+5)& = & -12 \color{red}{+} (-10-5x) \\\Leftrightarrow & -6x+15& = &-12-10-5x \\\Leftrightarrow & -6x \color{red}{+15} & = &-22 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+15} \color{blue}{-15} \color{blue}{+5x} & = &-22 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-15} \\\Leftrightarrow & -6x+5x& = &-22-15 \\\Leftrightarrow & -x& = &-37 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-37}{ \color{red}{-1} } \\\Leftrightarrow & x = 37 & & \\ & V = \left\{ 37 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (6x-7)& = & -5 \color{red}{+} (5+x) \\\Leftrightarrow & 12x-14& = &-5+5+x \\\Leftrightarrow & 12x \color{red}{-14} & = &0 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & 12x-x& = &0+14 \\\Leftrightarrow & 11x& = &14 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{14}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{14}{11} & & \\ & V = \left\{ \frac{14}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-4x-2)& = & -4 \color{red}{+} (4+x) \\\Leftrightarrow & -8x-4& = &-4+4+x \\\Leftrightarrow & -8x \color{red}{-4} & = &0 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -8x-x& = &0+4 \\\Leftrightarrow & -9x& = &4 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{4}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-4}{9} & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (6x-3)& = & -11 \color{red}{-} (-11+x) \\\Leftrightarrow & 30x-15& = &-11+11-x \\\Leftrightarrow & 30x \color{red}{-15} & = &0 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & 30x+x& = &0+15 \\\Leftrightarrow & 31x& = &15 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{15}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{15}{31} & & \\ & V = \left\{ \frac{15}{31} \right\} & \\\end{align}\)