Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (x+2)& = & -5 \color{red}{+} (-15+x) \\\Leftrightarrow & 2x+4& = &-5-15+x \\\Leftrightarrow & 2x \color{red}{+4} & = &-20 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 2x-x& = &-20-4 \\\Leftrightarrow & x& = &-24 \\ & V = \left\{ -24 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-6x-3)& = & 3 \color{red}{-} (-13+x) \\\Leftrightarrow & -12x-6& = &3+13-x \\\Leftrightarrow & -12x \color{red}{-6} & = &16 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -12x+x& = &16+6 \\\Leftrightarrow & -11x& = &22 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{22}{ \color{red}{-11} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (x+4)& = & -8 \color{red}{+} (11+x) \\\Leftrightarrow & 4x+16& = &-8+11+x \\\Leftrightarrow & 4x \color{red}{+16} & = &3 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & 4x-x& = &3-16 \\\Leftrightarrow & 3x& = &-13 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-13}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-13}{3} & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-3x+7)& = & 1 \color{red}{+} (8+x) \\\Leftrightarrow & -6x+14& = &1+8+x \\\Leftrightarrow & -6x \color{red}{+14} & = &9 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+14} \color{blue}{-14} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{-14} \\\Leftrightarrow & -6x-x& = &9-14 \\\Leftrightarrow & -7x& = &-5 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-5}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{5}{7} & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (2x+3)& = & 8 \color{red}{+} (-11+x) \\\Leftrightarrow & 8x+12& = &8-11+x \\\Leftrightarrow & 8x \color{red}{+12} & = &-3 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 8x-x& = &-3-12 \\\Leftrightarrow & 7x& = &-15 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-15}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-15}{7} & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-2x+5)& = & -12 \color{red}{+} (-14+x) \\\Leftrightarrow & -12x+30& = &-12-14+x \\\Leftrightarrow & -12x \color{red}{+30} & = &-26 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &-26 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -12x-x& = &-26-30 \\\Leftrightarrow & -13x& = &-56 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-56}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{56}{13} & & \\ & V = \left\{ \frac{56}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-5x+7)& = & -7 \color{red}{+} (11+3x) \\\Leftrightarrow & -20x+28& = &-7+11+3x \\\Leftrightarrow & -20x \color{red}{+28} & = &4 \color{red}{+3x} \\\Leftrightarrow & -20x \color{red}{+28} \color{blue}{-28} \color{blue}{-3x} & = &4 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-28} \\\Leftrightarrow & -20x-3x& = &4-28 \\\Leftrightarrow & -23x& = &-24 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-24}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{24}{23} & & \\ & V = \left\{ \frac{24}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (4x-1)& = & 5 \color{red}{-} (7+3x) \\\Leftrightarrow & 8x-2& = &5-7-3x \\\Leftrightarrow & 8x \color{red}{-2} & = &-2 \color{red}{-3x} \\\Leftrightarrow & 8x \color{red}{-2} \color{blue}{+2} \color{blue}{+3x} & = &-2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+2} \\\Leftrightarrow & 8x+3x& = &-2+2 \\\Leftrightarrow & 11x& = &0 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{0}{ \color{red}{11} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-x+4)& = & 11 \color{red}{-} (-7-3x) \\\Leftrightarrow & -4x+16& = &11+7+3x \\\Leftrightarrow & -4x \color{red}{+16} & = &18 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+16} \color{blue}{-16} \color{blue}{-3x} & = &18 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-16} \\\Leftrightarrow & -4x-3x& = &18-16 \\\Leftrightarrow & -7x& = &2 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{2}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-2}{7} & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (6x+2)& = & -6 \color{red}{+} (-11+x) \\\Leftrightarrow & 30x+10& = &-6-11+x \\\Leftrightarrow & 30x \color{red}{+10} & = &-17 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & 30x-x& = &-17-10 \\\Leftrightarrow & 29x& = &-27 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-27}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-27}{29} & & \\ & V = \left\{ \frac{-27}{29} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (4x+3)& = & -14 \color{red}{+} (10+x) \\\Leftrightarrow & 20x+15& = &-14+10+x \\\Leftrightarrow & 20x \color{red}{+15} & = &-4 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & 20x-x& = &-4-15 \\\Leftrightarrow & 19x& = &-19 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-19}{ \color{red}{19} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-2x+7)& = & -14 \color{red}{-} (7+x) \\\Leftrightarrow & -8x+28& = &-14-7-x \\\Leftrightarrow & -8x \color{red}{+28} & = &-21 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &-21 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & -8x+x& = &-21-28 \\\Leftrightarrow & -7x& = &-49 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-49}{ \color{red}{-7} } \\\Leftrightarrow & x = 7 & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)