Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-x-6)& = & -8 \color{red}{+} (11+x) \\\Leftrightarrow & -3x-18& = &-8+11+x \\\Leftrightarrow & -3x \color{red}{-18} & = &3 \color{red}{+x} \\\Leftrightarrow & -3x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & -3x-x& = &3+18 \\\Leftrightarrow & -4x& = &21 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{21}{ \color{red}{-4} } \\\Leftrightarrow & x = \frac{-21}{4} & & \\ & V = \left\{ \frac{-21}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (x-3)& = & 6 \color{red}{-} (8-2x) \\\Leftrightarrow & 3x-9& = &6-8+2x \\\Leftrightarrow & 3x \color{red}{-9} & = &-2 \color{red}{+2x} \\\Leftrightarrow & 3x \color{red}{-9} \color{blue}{+9} \color{blue}{-2x} & = &-2 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+9} \\\Leftrightarrow & 3x-2x& = &-2+9 \\\Leftrightarrow & x& = &7 \\ & V = \left\{ 7 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (3x-6)& = & 1 \color{red}{-} (-5+4x) \\\Leftrightarrow & 15x-30& = &1+5-4x \\\Leftrightarrow & 15x \color{red}{-30} & = &6 \color{red}{-4x} \\\Leftrightarrow & 15x \color{red}{-30} \color{blue}{+30} \color{blue}{+4x} & = &6 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+30} \\\Leftrightarrow & 15x+4x& = &6+30 \\\Leftrightarrow & 19x& = &36 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{36}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{36}{19} & & \\ & V = \left\{ \frac{36}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-4x-7)& = & 6 \color{red}{-} (4+x) \\\Leftrightarrow & -24x-42& = &6-4-x \\\Leftrightarrow & -24x \color{red}{-42} & = &2 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & -24x+x& = &2+42 \\\Leftrightarrow & -23x& = &44 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{44}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-44}{23} & & \\ & V = \left\{ \frac{-44}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (5x-4)& = & 7 \color{red}{+} (-15+x) \\\Leftrightarrow & 15x-12& = &7-15+x \\\Leftrightarrow & 15x \color{red}{-12} & = &-8 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 15x-x& = &-8+12 \\\Leftrightarrow & 14x& = &4 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{4}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{2}{7} & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-3x+7)& = & -6 \color{red}{-} (-7+4x) \\\Leftrightarrow & -9x+21& = &-6+7-4x \\\Leftrightarrow & -9x \color{red}{+21} & = &1 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{+21} \color{blue}{-21} \color{blue}{+4x} & = &1 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-21} \\\Leftrightarrow & -9x+4x& = &1-21 \\\Leftrightarrow & -5x& = &-20 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-20}{ \color{red}{-5} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-x+6)& = & 5 \color{red}{+} (-15-5x) \\\Leftrightarrow & -6x+36& = &5-15-5x \\\Leftrightarrow & -6x \color{red}{+36} & = &-10 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+36} \color{blue}{-36} \color{blue}{+5x} & = &-10 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-36} \\\Leftrightarrow & -6x+5x& = &-10-36 \\\Leftrightarrow & -x& = &-46 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-46}{ \color{red}{-1} } \\\Leftrightarrow & x = 46 & & \\ & V = \left\{ 46 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (x+6)& = & -1 \color{red}{-} (-10-5x) \\\Leftrightarrow & 6x+36& = &-1+10+5x \\\Leftrightarrow & 6x \color{red}{+36} & = &9 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+36} \color{blue}{-36} \color{blue}{-5x} & = &9 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-36} \\\Leftrightarrow & 6x-5x& = &9-36 \\\Leftrightarrow & x& = &-27 \\ & V = \left\{ -27 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (4x+4)& = & -12 \color{red}{+} (6-5x) \\\Leftrightarrow & 8x+8& = &-12+6-5x \\\Leftrightarrow & 8x \color{red}{+8} & = &-6 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{+8} \color{blue}{-8} \color{blue}{+5x} & = &-6 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-8} \\\Leftrightarrow & 8x+5x& = &-6-8 \\\Leftrightarrow & 13x& = &-14 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-14}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-14}{13} & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (3x+6)& = & -9 \color{red}{+} (-12+x) \\\Leftrightarrow & 15x+30& = &-9-12+x \\\Leftrightarrow & 15x \color{red}{+30} & = &-21 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &-21 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & 15x-x& = &-21-30 \\\Leftrightarrow & 14x& = &-51 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{-51}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{-51}{14} & & \\ & V = \left\{ \frac{-51}{14} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (6x+3)& = & 11 \color{red}{-} (6+x) \\\Leftrightarrow & 30x+15& = &11-6-x \\\Leftrightarrow & 30x \color{red}{+15} & = &5 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & 30x+x& = &5-15 \\\Leftrightarrow & 31x& = &-10 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-10}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-10}{31} & & \\ & V = \left\{ \frac{-10}{31} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (6x-2)& = & -13 \color{red}{+} (-6+x) \\\Leftrightarrow & 30x-10& = &-13-6+x \\\Leftrightarrow & 30x \color{red}{-10} & = &-19 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 30x-x& = &-19+10 \\\Leftrightarrow & 29x& = &-9 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-9}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-9}{29} & & \\ & V = \left\{ \frac{-9}{29} \right\} & \\\end{align}\)