Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (4x+6)& = & -5 \color{red}{-} (-8+3x) \\\Leftrightarrow & 8x+12& = &-5+8-3x \\\Leftrightarrow & 8x \color{red}{+12} & = &3 \color{red}{-3x} \\\Leftrightarrow & 8x \color{red}{+12} \color{blue}{-12} \color{blue}{+3x} & = &3 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-12} \\\Leftrightarrow & 8x+3x& = &3-12 \\\Leftrightarrow & 11x& = &-9 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-9}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-9}{11} & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-2x-4)& = & 1 \color{red}{+} (-8-3x) \\\Leftrightarrow & -10x-20& = &1-8-3x \\\Leftrightarrow & -10x \color{red}{-20} & = &-7 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{-20} \color{blue}{+20} \color{blue}{+3x} & = &-7 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+20} \\\Leftrightarrow & -10x+3x& = &-7+20 \\\Leftrightarrow & -7x& = &13 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{13}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-13}{7} & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (6x+1)& = & -11 \color{red}{-} (8+x) \\\Leftrightarrow & 12x+2& = &-11-8-x \\\Leftrightarrow & 12x \color{red}{+2} & = &-19 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & 12x+x& = &-19-2 \\\Leftrightarrow & 13x& = &-21 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-21}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-21}{13} & & \\ & V = \left\{ \frac{-21}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (6x+5)& = & -11 \color{red}{-} (13+x) \\\Leftrightarrow & 30x+25& = &-11-13-x \\\Leftrightarrow & 30x \color{red}{+25} & = &-24 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+25} \color{blue}{-25} \color{blue}{+x} & = &-24 \color{red}{-x} \color{blue}{+x} \color{blue}{-25} \\\Leftrightarrow & 30x+x& = &-24-25 \\\Leftrightarrow & 31x& = &-49 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-49}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-49}{31} & & \\ & V = \left\{ \frac{-49}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-x-1)& = & -3 \color{red}{-} (-10-4x) \\\Leftrightarrow & -5x-5& = &-3+10+4x \\\Leftrightarrow & -5x \color{red}{-5} & = &7 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{-5} \color{blue}{+5} \color{blue}{-4x} & = &7 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+5} \\\Leftrightarrow & -5x-4x& = &7+5 \\\Leftrightarrow & -9x& = &12 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{12}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-4}{3} & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (5x-6)& = & 8 \color{red}{+} (-15+2x) \\\Leftrightarrow & 25x-30& = &8-15+2x \\\Leftrightarrow & 25x \color{red}{-30} & = &-7 \color{red}{+2x} \\\Leftrightarrow & 25x \color{red}{-30} \color{blue}{+30} \color{blue}{-2x} & = &-7 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+30} \\\Leftrightarrow & 25x-2x& = &-7+30 \\\Leftrightarrow & 23x& = &23 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{23}{ \color{red}{23} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-6x-1)& = & 10 \color{red}{+} (-2+x) \\\Leftrightarrow & -12x-2& = &10-2+x \\\Leftrightarrow & -12x \color{red}{-2} & = &8 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & -12x-x& = &8+2 \\\Leftrightarrow & -13x& = &10 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{10}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-10}{13} & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (4x-3)& = & -9 \color{red}{+} (-13+x) \\\Leftrightarrow & 16x-12& = &-9-13+x \\\Leftrightarrow & 16x \color{red}{-12} & = &-22 \color{red}{+x} \\\Leftrightarrow & 16x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-22 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 16x-x& = &-22+12 \\\Leftrightarrow & 15x& = &-10 \\\Leftrightarrow & \frac{15x}{ \color{red}{15} }& = &\frac{-10}{ \color{red}{15} } \\\Leftrightarrow & x = \frac{-2}{3} & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (x-6)& = & 10 \color{red}{-} (12+2x) \\\Leftrightarrow & 5x-30& = &10-12-2x \\\Leftrightarrow & 5x \color{red}{-30} & = &-2 \color{red}{-2x} \\\Leftrightarrow & 5x \color{red}{-30} \color{blue}{+30} \color{blue}{+2x} & = &-2 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+30} \\\Leftrightarrow & 5x+2x& = &-2+30 \\\Leftrightarrow & 7x& = &28 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{28}{ \color{red}{7} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-6x+5)& = & 13 \color{red}{+} (-4+x) \\\Leftrightarrow & -30x+25& = &13-4+x \\\Leftrightarrow & -30x \color{red}{+25} & = &9 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+25} \color{blue}{-25} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{-25} \\\Leftrightarrow & -30x-x& = &9-25 \\\Leftrightarrow & -31x& = &-16 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-16}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{16}{31} & & \\ & V = \left\{ \frac{16}{31} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (6x+7)& = & -13 \color{red}{-} (6+x) \\\Leftrightarrow & 36x+42& = &-13-6-x \\\Leftrightarrow & 36x \color{red}{+42} & = &-19 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & 36x+x& = &-19-42 \\\Leftrightarrow & 37x& = &-61 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{-61}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{-61}{37} & & \\ & V = \left\{ \frac{-61}{37} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-x-2)& = & -12 \color{red}{+} (13+2x) \\\Leftrightarrow & -3x-6& = &-12+13+2x \\\Leftrightarrow & -3x \color{red}{-6} & = &1 \color{red}{+2x} \\\Leftrightarrow & -3x \color{red}{-6} \color{blue}{+6} \color{blue}{-2x} & = &1 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+6} \\\Leftrightarrow & -3x-2x& = &1+6 \\\Leftrightarrow & -5x& = &7 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{7}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-7}{5} & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)