Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-3x+1)& = & -13 \color{red}{+} (-4-2x) \\\Leftrightarrow & -15x+5& = &-13-4-2x \\\Leftrightarrow & -15x \color{red}{+5} & = &-17 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+5} \color{blue}{-5} \color{blue}{+2x} & = &-17 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-5} \\\Leftrightarrow & -15x+2x& = &-17-5 \\\Leftrightarrow & -13x& = &-22 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-22}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{22}{13} & & \\ & V = \left\{ \frac{22}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (x-3)& = & 6 \color{red}{-} (11-2x) \\\Leftrightarrow & 3x-9& = &6-11+2x \\\Leftrightarrow & 3x \color{red}{-9} & = &-5 \color{red}{+2x} \\\Leftrightarrow & 3x \color{red}{-9} \color{blue}{+9} \color{blue}{-2x} & = &-5 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+9} \\\Leftrightarrow & 3x-2x& = &-5+9 \\\Leftrightarrow & x& = &4 \\ & V = \left\{ 4 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-6x-6)& = & -11 \color{red}{+} (2+x) \\\Leftrightarrow & -30x-30& = &-11+2+x \\\Leftrightarrow & -30x \color{red}{-30} & = &-9 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -30x-x& = &-9+30 \\\Leftrightarrow & -31x& = &21 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{21}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-21}{31} & & \\ & V = \left\{ \frac{-21}{31} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-3x-4)& = & 12 \color{red}{+} (-9+x) \\\Leftrightarrow & -6x-8& = &12-9+x \\\Leftrightarrow & -6x \color{red}{-8} & = &3 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -6x-x& = &3+8 \\\Leftrightarrow & -7x& = &11 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{11}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-11}{7} & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-4x-5)& = & 13 \color{red}{-} (7+x) \\\Leftrightarrow & -24x-30& = &13-7-x \\\Leftrightarrow & -24x \color{red}{-30} & = &6 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & -24x+x& = &6+30 \\\Leftrightarrow & -23x& = &36 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{36}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-36}{23} & & \\ & V = \left\{ \frac{-36}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (2x-6)& = & -11 \color{red}{+} (-14+3x) \\\Leftrightarrow & 10x-30& = &-11-14+3x \\\Leftrightarrow & 10x \color{red}{-30} & = &-25 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-30} \color{blue}{+30} \color{blue}{-3x} & = &-25 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+30} \\\Leftrightarrow & 10x-3x& = &-25+30 \\\Leftrightarrow & 7x& = &5 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{5}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{5}{7} & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-4x+7)& = & 7 \color{red}{-} (-2+x) \\\Leftrightarrow & -20x+35& = &7+2-x \\\Leftrightarrow & -20x \color{red}{+35} & = &9 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+35} \color{blue}{-35} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{-35} \\\Leftrightarrow & -20x+x& = &9-35 \\\Leftrightarrow & -19x& = &-26 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-26}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{26}{19} & & \\ & V = \left\{ \frac{26}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-6x-2)& = & 13 \color{red}{-} (12+x) \\\Leftrightarrow & -30x-10& = &13-12-x \\\Leftrightarrow & -30x \color{red}{-10} & = &1 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & -30x+x& = &1+10 \\\Leftrightarrow & -29x& = &11 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{11}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-11}{29} & & \\ & V = \left\{ \frac{-11}{29} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (4x-7)& = & 14 \color{red}{+} (-8+x) \\\Leftrightarrow & 24x-42& = &14-8+x \\\Leftrightarrow & 24x \color{red}{-42} & = &6 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & 24x-x& = &6+42 \\\Leftrightarrow & 23x& = &48 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{48}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{48}{23} & & \\ & V = \left\{ \frac{48}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-3x+4)& = & -14 \color{red}{-} (-6+x) \\\Leftrightarrow & -12x+16& = &-14+6-x \\\Leftrightarrow & -12x \color{red}{+16} & = &-8 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & -12x+x& = &-8-16 \\\Leftrightarrow & -11x& = &-24 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-24}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{24}{11} & & \\ & V = \left\{ \frac{24}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (3x+1)& = & -12 \color{red}{+} (6+x) \\\Leftrightarrow & 12x+4& = &-12+6+x \\\Leftrightarrow & 12x \color{red}{+4} & = &-6 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 12x-x& = &-6-4 \\\Leftrightarrow & 11x& = &-10 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-10}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-10}{11} & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-5x+2)& = & -1 \color{red}{-} (3+x) \\\Leftrightarrow & -15x+6& = &-1-3-x \\\Leftrightarrow & -15x \color{red}{+6} & = &-4 \color{red}{-x} \\\Leftrightarrow & -15x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -15x+x& = &-4-6 \\\Leftrightarrow & -14x& = &-10 \\\Leftrightarrow & \frac{-14x}{ \color{red}{-14} }& = &\frac{-10}{ \color{red}{-14} } \\\Leftrightarrow & x = \frac{5}{7} & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)