Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (5x+4)& = & -10 \color{red}{+} (5+3x) \\\Leftrightarrow & 20x+16& = &-10+5+3x \\\Leftrightarrow & 20x \color{red}{+16} & = &-5 \color{red}{+3x} \\\Leftrightarrow & 20x \color{red}{+16} \color{blue}{-16} \color{blue}{-3x} & = &-5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-16} \\\Leftrightarrow & 20x-3x& = &-5-16 \\\Leftrightarrow & 17x& = &-21 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-21}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-21}{17} & & \\ & V = \left\{ \frac{-21}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-x-2)& = & 4 \color{red}{+} (-9+x) \\\Leftrightarrow & -4x-8& = &4-9+x \\\Leftrightarrow & -4x \color{red}{-8} & = &-5 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -4x-x& = &-5+8 \\\Leftrightarrow & -5x& = &3 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{3}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-3}{5} & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-6x-4)& = & 7 \color{red}{-} (-5+x) \\\Leftrightarrow & -36x-24& = &7+5-x \\\Leftrightarrow & -36x \color{red}{-24} & = &12 \color{red}{-x} \\\Leftrightarrow & -36x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -36x+x& = &12+24 \\\Leftrightarrow & -35x& = &36 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = &\frac{36}{ \color{red}{-35} } \\\Leftrightarrow & x = \frac{-36}{35} & & \\ & V = \left\{ \frac{-36}{35} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (5x-7)& = & -11 \color{red}{-} (15+x) \\\Leftrightarrow & 20x-28& = &-11-15-x \\\Leftrightarrow & 20x \color{red}{-28} & = &-26 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &-26 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & 20x+x& = &-26+28 \\\Leftrightarrow & 21x& = &2 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{2}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{2}{21} & & \\ & V = \left\{ \frac{2}{21} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (5x+5)& = & -7 \color{red}{-} (7+x) \\\Leftrightarrow & 10x+10& = &-7-7-x \\\Leftrightarrow & 10x \color{red}{+10} & = &-14 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 10x+x& = &-14-10 \\\Leftrightarrow & 11x& = &-24 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-24}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-24}{11} & & \\ & V = \left\{ \frac{-24}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (x-7)& = & -5 \color{red}{-} (-7-4x) \\\Leftrightarrow & 5x-35& = &-5+7+4x \\\Leftrightarrow & 5x \color{red}{-35} & = &2 \color{red}{+4x} \\\Leftrightarrow & 5x \color{red}{-35} \color{blue}{+35} \color{blue}{-4x} & = &2 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+35} \\\Leftrightarrow & 5x-4x& = &2+35 \\\Leftrightarrow & x& = &37 \\ & V = \left\{ 37 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (4x+7)& = & 11 \color{red}{-} (-8+x) \\\Leftrightarrow & 24x+42& = &11+8-x \\\Leftrightarrow & 24x \color{red}{+42} & = &19 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &19 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & 24x+x& = &19-42 \\\Leftrightarrow & 25x& = &-23 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-23}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-23}{25} & & \\ & V = \left\{ \frac{-23}{25} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (6x-4)& = & 1 \color{red}{+} (-14+x) \\\Leftrightarrow & 12x-8& = &1-14+x \\\Leftrightarrow & 12x \color{red}{-8} & = &-13 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & 12x-x& = &-13+8 \\\Leftrightarrow & 11x& = &-5 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-5}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-5}{11} & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-6x+3)& = & 5 \color{red}{-} (2+x) \\\Leftrightarrow & -24x+12& = &5-2-x \\\Leftrightarrow & -24x \color{red}{+12} & = &3 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -24x+x& = &3-12 \\\Leftrightarrow & -23x& = &-9 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-9}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{9}{23} & & \\ & V = \left\{ \frac{9}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (2x-3)& = & 11 \color{red}{-} (-6+x) \\\Leftrightarrow & 12x-18& = &11+6-x \\\Leftrightarrow & 12x \color{red}{-18} & = &17 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 12x+x& = &17+18 \\\Leftrightarrow & 13x& = &35 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{35}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{35}{13} & & \\ & V = \left\{ \frac{35}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-6x+5)& = & -6 \color{red}{+} (14-5x) \\\Leftrightarrow & -36x+30& = &-6+14-5x \\\Leftrightarrow & -36x \color{red}{+30} & = &8 \color{red}{-5x} \\\Leftrightarrow & -36x \color{red}{+30} \color{blue}{-30} \color{blue}{+5x} & = &8 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-30} \\\Leftrightarrow & -36x+5x& = &8-30 \\\Leftrightarrow & -31x& = &-22 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-22}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{22}{31} & & \\ & V = \left\{ \frac{22}{31} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (5x+3)& = & -1 \color{red}{+} (-10+x) \\\Leftrightarrow & 15x+9& = &-1-10+x \\\Leftrightarrow & 15x \color{red}{+9} & = &-11 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{+9} \color{blue}{-9} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{-9} \\\Leftrightarrow & 15x-x& = &-11-9 \\\Leftrightarrow & 14x& = &-20 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{-20}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{-10}{7} & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)