Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (2x-7)& = & -5 \color{red}{+} (4+x) \\\Leftrightarrow & 12x-42& = &-5+4+x \\\Leftrightarrow & 12x \color{red}{-42} & = &-1 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & 12x-x& = &-1+42 \\\Leftrightarrow & 11x& = &41 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{41}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{41}{11} & & \\ & V = \left\{ \frac{41}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (x+7)& = & 11 \color{red}{+} (-10+x) \\\Leftrightarrow & 5x+35& = &11-10+x \\\Leftrightarrow & 5x \color{red}{+35} & = &1 \color{red}{+x} \\\Leftrightarrow & 5x \color{red}{+35} \color{blue}{-35} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-35} \\\Leftrightarrow & 5x-x& = &1-35 \\\Leftrightarrow & 4x& = &-34 \\\Leftrightarrow & \frac{4x}{ \color{red}{4} }& = &\frac{-34}{ \color{red}{4} } \\\Leftrightarrow & x = \frac{-17}{2} & & \\ & V = \left\{ \frac{-17}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-3x+1)& = & 6 \color{red}{+} (4-5x) \\\Leftrightarrow & -18x+6& = &6+4-5x \\\Leftrightarrow & -18x \color{red}{+6} & = &10 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &10 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & -18x+5x& = &10-6 \\\Leftrightarrow & -13x& = &4 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{4}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-4}{13} & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-6x+3)& = & -11 \color{red}{-} (10-5x) \\\Leftrightarrow & -18x+9& = &-11-10+5x \\\Leftrightarrow & -18x \color{red}{+9} & = &-21 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+9} \color{blue}{-9} \color{blue}{-5x} & = &-21 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-9} \\\Leftrightarrow & -18x-5x& = &-21-9 \\\Leftrightarrow & -23x& = &-30 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-30}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{30}{23} & & \\ & V = \left\{ \frac{30}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-x+1)& = & -3 \color{red}{-} (-3+4x) \\\Leftrightarrow & -5x+5& = &-3+3-4x \\\Leftrightarrow & -5x \color{red}{+5} & = &0 \color{red}{-4x} \\\Leftrightarrow & -5x \color{red}{+5} \color{blue}{-5} \color{blue}{+4x} & = &0 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-5} \\\Leftrightarrow & -5x+4x& = &0-5 \\\Leftrightarrow & -x& = &-5 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-5}{ \color{red}{-1} } \\\Leftrightarrow & x = 5 & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-6x+1)& = & 15 \color{red}{+} (3-5x) \\\Leftrightarrow & -36x+6& = &15+3-5x \\\Leftrightarrow & -36x \color{red}{+6} & = &18 \color{red}{-5x} \\\Leftrightarrow & -36x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &18 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & -36x+5x& = &18-6 \\\Leftrightarrow & -31x& = &12 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{12}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-12}{31} & & \\ & V = \left\{ \frac{-12}{31} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (x-4)& = & 5 \color{red}{-} (14+x) \\\Leftrightarrow & 6x-24& = &5-14-x \\\Leftrightarrow & 6x \color{red}{-24} & = &-9 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 6x+x& = &-9+24 \\\Leftrightarrow & 7x& = &15 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{15}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{15}{7} & & \\ & V = \left\{ \frac{15}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (4x+7)& = & -10 \color{red}{+} (-9+x) \\\Leftrightarrow & 8x+14& = &-10-9+x \\\Leftrightarrow & 8x \color{red}{+14} & = &-19 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{+14} \color{blue}{-14} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{-14} \\\Leftrightarrow & 8x-x& = &-19-14 \\\Leftrightarrow & 7x& = &-33 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-33}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-33}{7} & & \\ & V = \left\{ \frac{-33}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (4x-1)& = & -6 \color{red}{-} (14+x) \\\Leftrightarrow & 24x-6& = &-6-14-x \\\Leftrightarrow & 24x \color{red}{-6} & = &-20 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 24x+x& = &-20+6 \\\Leftrightarrow & 25x& = &-14 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-14}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-14}{25} & & \\ & V = \left\{ \frac{-14}{25} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-4x+2)& = & 14 \color{red}{+} (13+x) \\\Leftrightarrow & -20x+10& = &14+13+x \\\Leftrightarrow & -20x \color{red}{+10} & = &27 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &27 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & -20x-x& = &27-10 \\\Leftrightarrow & -21x& = &17 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{17}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-17}{21} & & \\ & V = \left\{ \frac{-17}{21} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (4x-1)& = & -9 \color{red}{-} (11+3x) \\\Leftrightarrow & 8x-2& = &-9-11-3x \\\Leftrightarrow & 8x \color{red}{-2} & = &-20 \color{red}{-3x} \\\Leftrightarrow & 8x \color{red}{-2} \color{blue}{+2} \color{blue}{+3x} & = &-20 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+2} \\\Leftrightarrow & 8x+3x& = &-20+2 \\\Leftrightarrow & 11x& = &-18 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-18}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-18}{11} & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (2x-7)& = & 7 \color{red}{-} (8+x) \\\Leftrightarrow & 10x-35& = &7-8-x \\\Leftrightarrow & 10x \color{red}{-35} & = &-1 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{-35} \color{blue}{+35} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+35} \\\Leftrightarrow & 10x+x& = &-1+35 \\\Leftrightarrow & 11x& = &34 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{34}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{34}{11} & & \\ & V = \left\{ \frac{34}{11} \right\} & \\\end{align}\)