Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (4x-4)& = & -7 \color{red}{-} (3+x) \\\Leftrightarrow & 24x-24& = &-7-3-x \\\Leftrightarrow & 24x \color{red}{-24} & = &-10 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 24x+x& = &-10+24 \\\Leftrightarrow & 25x& = &14 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{14}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{14}{25} & & \\ & V = \left\{ \frac{14}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (3x+6)& = & -2 \color{red}{+} (10-4x) \\\Leftrightarrow & 9x+18& = &-2+10-4x \\\Leftrightarrow & 9x \color{red}{+18} & = &8 \color{red}{-4x} \\\Leftrightarrow & 9x \color{red}{+18} \color{blue}{-18} \color{blue}{+4x} & = &8 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-18} \\\Leftrightarrow & 9x+4x& = &8-18 \\\Leftrightarrow & 13x& = &-10 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-10}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-10}{13} & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-3x-7)& = & -15 \color{red}{-} (12+x) \\\Leftrightarrow & -6x-14& = &-15-12-x \\\Leftrightarrow & -6x \color{red}{-14} & = &-27 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &-27 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & -6x+x& = &-27+14 \\\Leftrightarrow & -5x& = &-13 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-13}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{13}{5} & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (4x-5)& = & 15 \color{red}{+} (8-5x) \\\Leftrightarrow & 8x-10& = &15+8-5x \\\Leftrightarrow & 8x \color{red}{-10} & = &23 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{-10} \color{blue}{+10} \color{blue}{+5x} & = &23 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+10} \\\Leftrightarrow & 8x+5x& = &23+10 \\\Leftrightarrow & 13x& = &33 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{33}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{33}{13} & & \\ & V = \left\{ \frac{33}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-2x-4)& = & 10 \color{red}{-} (-11-3x) \\\Leftrightarrow & -10x-20& = &10+11+3x \\\Leftrightarrow & -10x \color{red}{-20} & = &21 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-20} \color{blue}{+20} \color{blue}{-3x} & = &21 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+20} \\\Leftrightarrow & -10x-3x& = &21+20 \\\Leftrightarrow & -13x& = &41 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{41}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-41}{13} & & \\ & V = \left\{ \frac{-41}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-x+4)& = & -3 \color{red}{+} (7+x) \\\Leftrightarrow & -6x+24& = &-3+7+x \\\Leftrightarrow & -6x \color{red}{+24} & = &4 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -6x-x& = &4-24 \\\Leftrightarrow & -7x& = &-20 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-20}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{20}{7} & & \\ & V = \left\{ \frac{20}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (2x+4)& = & 4 \color{red}{-} (8+x) \\\Leftrightarrow & 12x+24& = &4-8-x \\\Leftrightarrow & 12x \color{red}{+24} & = &-4 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 12x+x& = &-4-24 \\\Leftrightarrow & 13x& = &-28 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-28}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-28}{13} & & \\ & V = \left\{ \frac{-28}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (5x-7)& = & 8 \color{red}{+} (14+x) \\\Leftrightarrow & 20x-28& = &8+14+x \\\Leftrightarrow & 20x \color{red}{-28} & = &22 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &22 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & 20x-x& = &22+28 \\\Leftrightarrow & 19x& = &50 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{50}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{50}{19} & & \\ & V = \left\{ \frac{50}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (5x+1)& = & -12 \color{red}{-} (4-2x) \\\Leftrightarrow & 25x+5& = &-12-4+2x \\\Leftrightarrow & 25x \color{red}{+5} & = &-16 \color{red}{+2x} \\\Leftrightarrow & 25x \color{red}{+5} \color{blue}{-5} \color{blue}{-2x} & = &-16 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-5} \\\Leftrightarrow & 25x-2x& = &-16-5 \\\Leftrightarrow & 23x& = &-21 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-21}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-21}{23} & & \\ & V = \left\{ \frac{-21}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (x-2)& = & 6 \color{red}{-} (-5+x) \\\Leftrightarrow & 2x-4& = &6+5-x \\\Leftrightarrow & 2x \color{red}{-4} & = &11 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 2x+x& = &11+4 \\\Leftrightarrow & 3x& = &15 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{15}{ \color{red}{3} } \\\Leftrightarrow & x = 5 & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-6x-4)& = & 12 \color{red}{+} (-1-5x) \\\Leftrightarrow & -18x-12& = &12-1-5x \\\Leftrightarrow & -18x \color{red}{-12} & = &11 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &11 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & -18x+5x& = &11+12 \\\Leftrightarrow & -13x& = &23 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{23}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-23}{13} & & \\ & V = \left\{ \frac{-23}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (3x+1)& = & -8 \color{red}{+} (-10-5x) \\\Leftrightarrow & 18x+6& = &-8-10-5x \\\Leftrightarrow & 18x \color{red}{+6} & = &-18 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &-18 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & 18x+5x& = &-18-6 \\\Leftrightarrow & 23x& = &-24 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-24}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-24}{23} & & \\ & V = \left\{ \frac{-24}{23} \right\} & \\\end{align}\)