Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-x+1)& = & -2 \color{red}{+} (-15-5x) \\\Leftrightarrow & -6x+6& = &-2-15-5x \\\Leftrightarrow & -6x \color{red}{+6} & = &-17 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &-17 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & -6x+5x& = &-17-6 \\\Leftrightarrow & -x& = &-23 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-23}{ \color{red}{-1} } \\\Leftrightarrow & x = 23 & & \\ & V = \left\{ 23 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-3x+5)& = & 8 \color{red}{+} (-6-2x) \\\Leftrightarrow & -15x+25& = &8-6-2x \\\Leftrightarrow & -15x \color{red}{+25} & = &2 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+25} \color{blue}{-25} \color{blue}{+2x} & = &2 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-25} \\\Leftrightarrow & -15x+2x& = &2-25 \\\Leftrightarrow & -13x& = &-23 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-23}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{23}{13} & & \\ & V = \left\{ \frac{23}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (3x-1)& = & -10 \color{red}{+} (-7+x) \\\Leftrightarrow & 18x-6& = &-10-7+x \\\Leftrightarrow & 18x \color{red}{-6} & = &-17 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 18x-x& = &-17+6 \\\Leftrightarrow & 17x& = &-11 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-11}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-11}{17} & & \\ & V = \left\{ \frac{-11}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-4x-5)& = & 1 \color{red}{-} (-13+x) \\\Leftrightarrow & -24x-30& = &1+13-x \\\Leftrightarrow & -24x \color{red}{-30} & = &14 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & -24x+x& = &14+30 \\\Leftrightarrow & -23x& = &44 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{44}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-44}{23} & & \\ & V = \left\{ \frac{-44}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-4x-3)& = & -10 \color{red}{-} (-5+x) \\\Leftrightarrow & -24x-18& = &-10+5-x \\\Leftrightarrow & -24x \color{red}{-18} & = &-5 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -24x+x& = &-5+18 \\\Leftrightarrow & -23x& = &13 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{13}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-13}{23} & & \\ & V = \left\{ \frac{-13}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-6x-1)& = & -6 \color{red}{+} (5+x) \\\Leftrightarrow & -18x-3& = &-6+5+x \\\Leftrightarrow & -18x \color{red}{-3} & = &-1 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & -18x-x& = &-1+3 \\\Leftrightarrow & -19x& = &2 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{2}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-2}{19} & & \\ & V = \left\{ \frac{-2}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-5x-6)& = & 7 \color{red}{-} (-9-2x) \\\Leftrightarrow & -15x-18& = &7+9+2x \\\Leftrightarrow & -15x \color{red}{-18} & = &16 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{-18} \color{blue}{+18} \color{blue}{-2x} & = &16 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+18} \\\Leftrightarrow & -15x-2x& = &16+18 \\\Leftrightarrow & -17x& = &34 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{34}{ \color{red}{-17} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-4x+3)& = & 11 \color{red}{-} (-2+x) \\\Leftrightarrow & -8x+6& = &11+2-x \\\Leftrightarrow & -8x \color{red}{+6} & = &13 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -8x+x& = &13-6 \\\Leftrightarrow & -7x& = &7 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{7}{ \color{red}{-7} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (6x-6)& = & 7 \color{red}{-} (-4+x) \\\Leftrightarrow & 24x-24& = &7+4-x \\\Leftrightarrow & 24x \color{red}{-24} & = &11 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 24x+x& = &11+24 \\\Leftrightarrow & 25x& = &35 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{35}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{7}{5} & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (3x+4)& = & 15 \color{red}{-} (12+4x) \\\Leftrightarrow & 15x+20& = &15-12-4x \\\Leftrightarrow & 15x \color{red}{+20} & = &3 \color{red}{-4x} \\\Leftrightarrow & 15x \color{red}{+20} \color{blue}{-20} \color{blue}{+4x} & = &3 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-20} \\\Leftrightarrow & 15x+4x& = &3-20 \\\Leftrightarrow & 19x& = &-17 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-17}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-17}{19} & & \\ & V = \left\{ \frac{-17}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (3x+6)& = & 7 \color{red}{+} (2+x) \\\Leftrightarrow & 12x+24& = &7+2+x \\\Leftrightarrow & 12x \color{red}{+24} & = &9 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 12x-x& = &9-24 \\\Leftrightarrow & 11x& = &-15 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-15}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-15}{11} & & \\ & V = \left\{ \frac{-15}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (4x+6)& = & 3 \color{red}{-} (-6+x) \\\Leftrightarrow & 8x+12& = &3+6-x \\\Leftrightarrow & 8x \color{red}{+12} & = &9 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 8x+x& = &9-12 \\\Leftrightarrow & 9x& = &-3 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-3}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-1}{3} & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)