Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-3x+5)& = & -11 \color{red}{+} (6-2x) \\\Leftrightarrow & -9x+15& = &-11+6-2x \\\Leftrightarrow & -9x \color{red}{+15} & = &-5 \color{red}{-2x} \\\Leftrightarrow & -9x \color{red}{+15} \color{blue}{-15} \color{blue}{+2x} & = &-5 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-15} \\\Leftrightarrow & -9x+2x& = &-5-15 \\\Leftrightarrow & -7x& = &-20 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-20}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{20}{7} & & \\ & V = \left\{ \frac{20}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-x+1)& = & -3 \color{red}{-} (15-2x) \\\Leftrightarrow & -5x+5& = &-3-15+2x \\\Leftrightarrow & -5x \color{red}{+5} & = &-18 \color{red}{+2x} \\\Leftrightarrow & -5x \color{red}{+5} \color{blue}{-5} \color{blue}{-2x} & = &-18 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-5} \\\Leftrightarrow & -5x-2x& = &-18-5 \\\Leftrightarrow & -7x& = &-23 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-23}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{23}{7} & & \\ & V = \left\{ \frac{23}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-3x+1)& = & 9 \color{red}{-} (6-2x) \\\Leftrightarrow & -15x+5& = &9-6+2x \\\Leftrightarrow & -15x \color{red}{+5} & = &3 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+5} \color{blue}{-5} \color{blue}{-2x} & = &3 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-5} \\\Leftrightarrow & -15x-2x& = &3-5 \\\Leftrightarrow & -17x& = &-2 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-2}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{2}{17} & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-6x+2)& = & -8 \color{red}{+} (-10+x) \\\Leftrightarrow & -18x+6& = &-8-10+x \\\Leftrightarrow & -18x \color{red}{+6} & = &-18 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-18 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -18x-x& = &-18-6 \\\Leftrightarrow & -19x& = &-24 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-24}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{24}{19} & & \\ & V = \left\{ \frac{24}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (6x+7)& = & 5 \color{red}{-} (-7+x) \\\Leftrightarrow & 24x+28& = &5+7-x \\\Leftrightarrow & 24x \color{red}{+28} & = &12 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & 24x+x& = &12-28 \\\Leftrightarrow & 25x& = &-16 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-16}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-16}{25} & & \\ & V = \left\{ \frac{-16}{25} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (4x-3)& = & -2 \color{red}{-} (6+3x) \\\Leftrightarrow & 16x-12& = &-2-6-3x \\\Leftrightarrow & 16x \color{red}{-12} & = &-8 \color{red}{-3x} \\\Leftrightarrow & 16x \color{red}{-12} \color{blue}{+12} \color{blue}{+3x} & = &-8 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+12} \\\Leftrightarrow & 16x+3x& = &-8+12 \\\Leftrightarrow & 19x& = &4 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{4}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{4}{19} & & \\ & V = \left\{ \frac{4}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-4x+3)& = & 10 \color{red}{+} (1+x) \\\Leftrightarrow & -24x+18& = &10+1+x \\\Leftrightarrow & -24x \color{red}{+18} & = &11 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & -24x-x& = &11-18 \\\Leftrightarrow & -25x& = &-7 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-7}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{7}{25} & & \\ & V = \left\{ \frac{7}{25} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (x+1)& = & -15 \color{red}{+} (15+x) \\\Leftrightarrow & 3x+3& = &-15+15+x \\\Leftrightarrow & 3x \color{red}{+3} & = &0 \color{red}{+x} \\\Leftrightarrow & 3x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & 3x-x& = &0-3 \\\Leftrightarrow & 2x& = &-3 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{-3}{ \color{red}{2} } \\\Leftrightarrow & x = \frac{-3}{2} & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-x-2)& = & -15 \color{red}{-} (-10+x) \\\Leftrightarrow & -6x-12& = &-15+10-x \\\Leftrightarrow & -6x \color{red}{-12} & = &-5 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -6x+x& = &-5+12 \\\Leftrightarrow & -5x& = &7 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{7}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-7}{5} & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (6x-5)& = & 2 \color{red}{+} (5+x) \\\Leftrightarrow & 36x-30& = &2+5+x \\\Leftrightarrow & 36x \color{red}{-30} & = &7 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 36x-x& = &7+30 \\\Leftrightarrow & 35x& = &37 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{37}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{37}{35} & & \\ & V = \left\{ \frac{37}{35} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (2x-2)& = & 10 \color{red}{-} (7+x) \\\Leftrightarrow & 12x-12& = &10-7-x \\\Leftrightarrow & 12x \color{red}{-12} & = &3 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 12x+x& = &3+12 \\\Leftrightarrow & 13x& = &15 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{15}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{15}{13} & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (5x-3)& = & -10 \color{red}{+} (-13+x) \\\Leftrightarrow & 20x-12& = &-10-13+x \\\Leftrightarrow & 20x \color{red}{-12} & = &-23 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-23 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 20x-x& = &-23+12 \\\Leftrightarrow & 19x& = &-11 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-11}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-11}{19} & & \\ & V = \left\{ \frac{-11}{19} \right\} & \\\end{align}\)