Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-6x-2)& = & -7 \color{red}{+} (-13+x) \\\Leftrightarrow & -18x-6& = &-7-13+x \\\Leftrightarrow & -18x \color{red}{-6} & = &-20 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -18x-x& = &-20+6 \\\Leftrightarrow & -19x& = &-14 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-14}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{14}{19} & & \\ & V = \left\{ \frac{14}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-3x+5)& = & 10 \color{red}{+} (-10+x) \\\Leftrightarrow & -12x+20& = &10-10+x \\\Leftrightarrow & -12x \color{red}{+20} & = &0 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & -12x-x& = &0-20 \\\Leftrightarrow & -13x& = &-20 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-20}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{20}{13} & & \\ & V = \left\{ \frac{20}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-4x-6)& = & 13 \color{red}{+} (-13+3x) \\\Leftrightarrow & -16x-24& = &13-13+3x \\\Leftrightarrow & -16x \color{red}{-24} & = &0 \color{red}{+3x} \\\Leftrightarrow & -16x \color{red}{-24} \color{blue}{+24} \color{blue}{-3x} & = &0 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+24} \\\Leftrightarrow & -16x-3x& = &0+24 \\\Leftrightarrow & -19x& = &24 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{24}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-24}{19} & & \\ & V = \left\{ \frac{-24}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-2x+5)& = & -15 \color{red}{+} (-9+3x) \\\Leftrightarrow & -4x+10& = &-15-9+3x \\\Leftrightarrow & -4x \color{red}{+10} & = &-24 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+10} \color{blue}{-10} \color{blue}{-3x} & = &-24 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-10} \\\Leftrightarrow & -4x-3x& = &-24-10 \\\Leftrightarrow & -7x& = &-34 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-34}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{34}{7} & & \\ & V = \left\{ \frac{34}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (2x-3)& = & 1 \color{red}{-} (8+x) \\\Leftrightarrow & 8x-12& = &1-8-x \\\Leftrightarrow & 8x \color{red}{-12} & = &-7 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 8x+x& = &-7+12 \\\Leftrightarrow & 9x& = &5 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{5}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{5}{9} & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-2x-4)& = & -11 \color{red}{-} (-1+x) \\\Leftrightarrow & -12x-24& = &-11+1-x \\\Leftrightarrow & -12x \color{red}{-24} & = &-10 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -12x+x& = &-10+24 \\\Leftrightarrow & -11x& = &14 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{14}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-14}{11} & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (2x+2)& = & -8 \color{red}{+} (2-3x) \\\Leftrightarrow & 4x+4& = &-8+2-3x \\\Leftrightarrow & 4x \color{red}{+4} & = &-6 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+4} \color{blue}{-4} \color{blue}{+3x} & = &-6 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-4} \\\Leftrightarrow & 4x+3x& = &-6-4 \\\Leftrightarrow & 7x& = &-10 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-10}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-10}{7} & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (3x-6)& = & 14 \color{red}{+} (4-5x) \\\Leftrightarrow & 18x-36& = &14+4-5x \\\Leftrightarrow & 18x \color{red}{-36} & = &18 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-36} \color{blue}{+36} \color{blue}{+5x} & = &18 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+36} \\\Leftrightarrow & 18x+5x& = &18+36 \\\Leftrightarrow & 23x& = &54 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{54}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{54}{23} & & \\ & V = \left\{ \frac{54}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-5x+4)& = & -2 \color{red}{-} (6-4x) \\\Leftrightarrow & -25x+20& = &-2-6+4x \\\Leftrightarrow & -25x \color{red}{+20} & = &-8 \color{red}{+4x} \\\Leftrightarrow & -25x \color{red}{+20} \color{blue}{-20} \color{blue}{-4x} & = &-8 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-20} \\\Leftrightarrow & -25x-4x& = &-8-20 \\\Leftrightarrow & -29x& = &-28 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-28}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{28}{29} & & \\ & V = \left\{ \frac{28}{29} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-5x-2)& = & 1 \color{red}{+} (-4+4x) \\\Leftrightarrow & -25x-10& = &1-4+4x \\\Leftrightarrow & -25x \color{red}{-10} & = &-3 \color{red}{+4x} \\\Leftrightarrow & -25x \color{red}{-10} \color{blue}{+10} \color{blue}{-4x} & = &-3 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+10} \\\Leftrightarrow & -25x-4x& = &-3+10 \\\Leftrightarrow & -29x& = &7 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{7}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-7}{29} & & \\ & V = \left\{ \frac{-7}{29} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-5x-1)& = & 4 \color{red}{-} (13+x) \\\Leftrightarrow & -20x-4& = &4-13-x \\\Leftrightarrow & -20x \color{red}{-4} & = &-9 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -20x+x& = &-9+4 \\\Leftrightarrow & -19x& = &-5 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-5}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{5}{19} & & \\ & V = \left\{ \frac{5}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (5x+4)& = & -15 \color{red}{+} (2+x) \\\Leftrightarrow & 20x+16& = &-15+2+x \\\Leftrightarrow & 20x \color{red}{+16} & = &-13 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & 20x-x& = &-13-16 \\\Leftrightarrow & 19x& = &-29 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-29}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-29}{19} & & \\ & V = \left\{ \frac{-29}{19} \right\} & \\\end{align}\)