Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (6x-4)& = & 6 \color{red}{+} (-14-5x) \\\Leftrightarrow & 18x-12& = &6-14-5x \\\Leftrightarrow & 18x \color{red}{-12} & = &-8 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &-8 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & 18x+5x& = &-8+12 \\\Leftrightarrow & 23x& = &4 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{4}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{4}{23} & & \\ & V = \left\{ \frac{4}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (6x-7)& = & 3 \color{red}{+} (-13-5x) \\\Leftrightarrow & 36x-42& = &3-13-5x \\\Leftrightarrow & 36x \color{red}{-42} & = &-10 \color{red}{-5x} \\\Leftrightarrow & 36x \color{red}{-42} \color{blue}{+42} \color{blue}{+5x} & = &-10 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+42} \\\Leftrightarrow & 36x+5x& = &-10+42 \\\Leftrightarrow & 41x& = &32 \\\Leftrightarrow & \frac{41x}{ \color{red}{41} }& = &\frac{32}{ \color{red}{41} } \\\Leftrightarrow & x = \frac{32}{41} & & \\ & V = \left\{ \frac{32}{41} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-5x-3)& = & -15 \color{red}{-} (4+x) \\\Leftrightarrow & -30x-18& = &-15-4-x \\\Leftrightarrow & -30x \color{red}{-18} & = &-19 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -30x+x& = &-19+18 \\\Leftrightarrow & -29x& = &-1 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-1}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{1}{29} & & \\ & V = \left\{ \frac{1}{29} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (2x-5)& = & 3 \color{red}{-} (4+x) \\\Leftrightarrow & 6x-15& = &3-4-x \\\Leftrightarrow & 6x \color{red}{-15} & = &-1 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & 6x+x& = &-1+15 \\\Leftrightarrow & 7x& = &14 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{14}{ \color{red}{7} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (6x-1)& = & -8 \color{red}{-} (15+x) \\\Leftrightarrow & 30x-5& = &-8-15-x \\\Leftrightarrow & 30x \color{red}{-5} & = &-23 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-5} \color{blue}{+5} \color{blue}{+x} & = &-23 \color{red}{-x} \color{blue}{+x} \color{blue}{+5} \\\Leftrightarrow & 30x+x& = &-23+5 \\\Leftrightarrow & 31x& = &-18 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-18}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-18}{31} & & \\ & V = \left\{ \frac{-18}{31} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (6x-2)& = & -6 \color{red}{-} (-10-5x) \\\Leftrightarrow & 36x-12& = &-6+10+5x \\\Leftrightarrow & 36x \color{red}{-12} & = &4 \color{red}{+5x} \\\Leftrightarrow & 36x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &4 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & 36x-5x& = &4+12 \\\Leftrightarrow & 31x& = &16 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{16}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{16}{31} & & \\ & V = \left\{ \frac{16}{31} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-3x-2)& = & -5 \color{red}{-} (-8+x) \\\Leftrightarrow & -15x-10& = &-5+8-x \\\Leftrightarrow & -15x \color{red}{-10} & = &3 \color{red}{-x} \\\Leftrightarrow & -15x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & -15x+x& = &3+10 \\\Leftrightarrow & -14x& = &13 \\\Leftrightarrow & \frac{-14x}{ \color{red}{-14} }& = &\frac{13}{ \color{red}{-14} } \\\Leftrightarrow & x = \frac{-13}{14} & & \\ & V = \left\{ \frac{-13}{14} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-5x-2)& = & -6 \color{red}{-} (-3+4x) \\\Leftrightarrow & -15x-6& = &-6+3-4x \\\Leftrightarrow & -15x \color{red}{-6} & = &-3 \color{red}{-4x} \\\Leftrightarrow & -15x \color{red}{-6} \color{blue}{+6} \color{blue}{+4x} & = &-3 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+6} \\\Leftrightarrow & -15x+4x& = &-3+6 \\\Leftrightarrow & -11x& = &3 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{3}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-3}{11} & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-4x+2)& = & -6 \color{red}{-} (-3+x) \\\Leftrightarrow & -20x+10& = &-6+3-x \\\Leftrightarrow & -20x \color{red}{+10} & = &-3 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & -20x+x& = &-3-10 \\\Leftrightarrow & -19x& = &-13 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-13}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{13}{19} & & \\ & V = \left\{ \frac{13}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-6x-2)& = & 10 \color{red}{-} (15+x) \\\Leftrightarrow & -24x-8& = &10-15-x \\\Leftrightarrow & -24x \color{red}{-8} & = &-5 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & -24x+x& = &-5+8 \\\Leftrightarrow & -23x& = &3 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{3}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-3}{23} & & \\ & V = \left\{ \frac{-3}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (6x+3)& = & -5 \color{red}{+} (4-5x) \\\Leftrightarrow & 18x+9& = &-5+4-5x \\\Leftrightarrow & 18x \color{red}{+9} & = &-1 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{+9} \color{blue}{-9} \color{blue}{+5x} & = &-1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-9} \\\Leftrightarrow & 18x+5x& = &-1-9 \\\Leftrightarrow & 23x& = &-10 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-10}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-10}{23} & & \\ & V = \left\{ \frac{-10}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (2x+4)& = & -6 \color{red}{-} (13-3x) \\\Leftrightarrow & 10x+20& = &-6-13+3x \\\Leftrightarrow & 10x \color{red}{+20} & = &-19 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+20} \color{blue}{-20} \color{blue}{-3x} & = &-19 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-20} \\\Leftrightarrow & 10x-3x& = &-19-20 \\\Leftrightarrow & 7x& = &-39 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-39}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-39}{7} & & \\ & V = \left\{ \frac{-39}{7} \right\} & \\\end{align}\)