Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-3x+5)& = & -14 \color{red}{+} (5-5x) \\\Leftrightarrow & -18x+30& = &-14+5-5x \\\Leftrightarrow & -18x \color{red}{+30} & = &-9 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{+30} \color{blue}{-30} \color{blue}{+5x} & = &-9 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-30} \\\Leftrightarrow & -18x+5x& = &-9-30 \\\Leftrightarrow & -13x& = &-39 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-39}{ \color{red}{-13} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-3x+7)& = & 6 \color{red}{+} (1+x) \\\Leftrightarrow & -18x+42& = &6+1+x \\\Leftrightarrow & -18x \color{red}{+42} & = &7 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & -18x-x& = &7-42 \\\Leftrightarrow & -19x& = &-35 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-35}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{35}{19} & & \\ & V = \left\{ \frac{35}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-4x+2)& = & 15 \color{red}{+} (6+x) \\\Leftrightarrow & -16x+8& = &15+6+x \\\Leftrightarrow & -16x \color{red}{+8} & = &21 \color{red}{+x} \\\Leftrightarrow & -16x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &21 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -16x-x& = &21-8 \\\Leftrightarrow & -17x& = &13 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{13}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-13}{17} & & \\ & V = \left\{ \frac{-13}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (5x-3)& = & 12 \color{red}{-} (-14+x) \\\Leftrightarrow & 30x-18& = &12+14-x \\\Leftrightarrow & 30x \color{red}{-18} & = &26 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &26 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 30x+x& = &26+18 \\\Leftrightarrow & 31x& = &44 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{44}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{44}{31} & & \\ & V = \left\{ \frac{44}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-3x+1)& = & -15 \color{red}{+} (14+x) \\\Leftrightarrow & -9x+3& = &-15+14+x \\\Leftrightarrow & -9x \color{red}{+3} & = &-1 \color{red}{+x} \\\Leftrightarrow & -9x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & -9x-x& = &-1-3 \\\Leftrightarrow & -10x& = &-4 \\\Leftrightarrow & \frac{-10x}{ \color{red}{-10} }& = &\frac{-4}{ \color{red}{-10} } \\\Leftrightarrow & x = \frac{2}{5} & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (x+6)& = & -1 \color{red}{-} (4+2x) \\\Leftrightarrow & 5x+30& = &-1-4-2x \\\Leftrightarrow & 5x \color{red}{+30} & = &-5 \color{red}{-2x} \\\Leftrightarrow & 5x \color{red}{+30} \color{blue}{-30} \color{blue}{+2x} & = &-5 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-30} \\\Leftrightarrow & 5x+2x& = &-5-30 \\\Leftrightarrow & 7x& = &-35 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-35}{ \color{red}{7} } \\\Leftrightarrow & x = -5 & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (2x+6)& = & -12 \color{red}{+} (-7-5x) \\\Leftrightarrow & 6x+18& = &-12-7-5x \\\Leftrightarrow & 6x \color{red}{+18} & = &-19 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+18} \color{blue}{-18} \color{blue}{+5x} & = &-19 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-18} \\\Leftrightarrow & 6x+5x& = &-19-18 \\\Leftrightarrow & 11x& = &-37 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-37}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-37}{11} & & \\ & V = \left\{ \frac{-37}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (2x+1)& = & -14 \color{red}{-} (-7-5x) \\\Leftrightarrow & 6x+3& = &-14+7+5x \\\Leftrightarrow & 6x \color{red}{+3} & = &-7 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+3} \color{blue}{-3} \color{blue}{-5x} & = &-7 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-3} \\\Leftrightarrow & 6x-5x& = &-7-3 \\\Leftrightarrow & x& = &-10 \\ & V = \left\{ -10 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (3x+4)& = & -6 \color{red}{+} (15+x) \\\Leftrightarrow & 18x+24& = &-6+15+x \\\Leftrightarrow & 18x \color{red}{+24} & = &9 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 18x-x& = &9-24 \\\Leftrightarrow & 17x& = &-15 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-15}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-15}{17} & & \\ & V = \left\{ \frac{-15}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (3x-4)& = & 15 \color{red}{+} (9-4x) \\\Leftrightarrow & 9x-12& = &15+9-4x \\\Leftrightarrow & 9x \color{red}{-12} & = &24 \color{red}{-4x} \\\Leftrightarrow & 9x \color{red}{-12} \color{blue}{+12} \color{blue}{+4x} & = &24 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+12} \\\Leftrightarrow & 9x+4x& = &24+12 \\\Leftrightarrow & 13x& = &36 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{36}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{36}{13} & & \\ & V = \left\{ \frac{36}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-6x-5)& = & -5 \color{red}{+} (-1+x) \\\Leftrightarrow & -24x-20& = &-5-1+x \\\Leftrightarrow & -24x \color{red}{-20} & = &-6 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & -24x-x& = &-6+20 \\\Leftrightarrow & -25x& = &14 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{14}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-14}{25} & & \\ & V = \left\{ \frac{-14}{25} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (3x-1)& = & 1 \color{red}{-} (14-2x) \\\Leftrightarrow & 15x-5& = &1-14+2x \\\Leftrightarrow & 15x \color{red}{-5} & = &-13 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{-5} \color{blue}{+5} \color{blue}{-2x} & = &-13 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+5} \\\Leftrightarrow & 15x-2x& = &-13+5 \\\Leftrightarrow & 13x& = &-8 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-8}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-8}{13} & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)