Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-6x+3)& = & -9 \color{red}{+} (6+x) \\\Leftrightarrow & -24x+12& = &-9+6+x \\\Leftrightarrow & -24x \color{red}{+12} & = &-3 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -24x-x& = &-3-12 \\\Leftrightarrow & -25x& = &-15 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-15}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{3}{5} & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (4x+6)& = & 12 \color{red}{+} (12+x) \\\Leftrightarrow & 20x+30& = &12+12+x \\\Leftrightarrow & 20x \color{red}{+30} & = &24 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &24 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & 20x-x& = &24-30 \\\Leftrightarrow & 19x& = &-6 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-6}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-6}{19} & & \\ & V = \left\{ \frac{-6}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-x-4)& = & 13 \color{red}{-} (11-3x) \\\Leftrightarrow & -4x-16& = &13-11+3x \\\Leftrightarrow & -4x \color{red}{-16} & = &2 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-16} \color{blue}{+16} \color{blue}{-3x} & = &2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+16} \\\Leftrightarrow & -4x-3x& = &2+16 \\\Leftrightarrow & -7x& = &18 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{18}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-18}{7} & & \\ & V = \left\{ \frac{-18}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (4x-1)& = & 15 \color{red}{-} (-12-3x) \\\Leftrightarrow & 16x-4& = &15+12+3x \\\Leftrightarrow & 16x \color{red}{-4} & = &27 \color{red}{+3x} \\\Leftrightarrow & 16x \color{red}{-4} \color{blue}{+4} \color{blue}{-3x} & = &27 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+4} \\\Leftrightarrow & 16x-3x& = &27+4 \\\Leftrightarrow & 13x& = &31 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{31}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{31}{13} & & \\ & V = \left\{ \frac{31}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-6x-1)& = & 5 \color{red}{-} (9+x) \\\Leftrightarrow & -24x-4& = &5-9-x \\\Leftrightarrow & -24x \color{red}{-4} & = &-4 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -24x+x& = &-4+4 \\\Leftrightarrow & -23x& = &0 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{0}{ \color{red}{-23} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (4x-3)& = & -5 \color{red}{+} (-1+x) \\\Leftrightarrow & 12x-9& = &-5-1+x \\\Leftrightarrow & 12x \color{red}{-9} & = &-6 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-9} \color{blue}{+9} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+9} \\\Leftrightarrow & 12x-x& = &-6+9 \\\Leftrightarrow & 11x& = &3 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{3}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{3}{11} & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-x+7)& = & 2 \color{red}{+} (1-5x) \\\Leftrightarrow & -3x+21& = &2+1-5x \\\Leftrightarrow & -3x \color{red}{+21} & = &3 \color{red}{-5x} \\\Leftrightarrow & -3x \color{red}{+21} \color{blue}{-21} \color{blue}{+5x} & = &3 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-21} \\\Leftrightarrow & -3x+5x& = &3-21 \\\Leftrightarrow & 2x& = &-18 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{-18}{ \color{red}{2} } \\\Leftrightarrow & x = -9 & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (5x+2)& = & 2 \color{red}{-} (-1+x) \\\Leftrightarrow & 20x+8& = &2+1-x \\\Leftrightarrow & 20x \color{red}{+8} & = &3 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 20x+x& = &3-8 \\\Leftrightarrow & 21x& = &-5 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-5}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-5}{21} & & \\ & V = \left\{ \frac{-5}{21} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-2x+6)& = & -11 \color{red}{-} (-5+x) \\\Leftrightarrow & -6x+18& = &-11+5-x \\\Leftrightarrow & -6x \color{red}{+18} & = &-6 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -6x+x& = &-6-18 \\\Leftrightarrow & -5x& = &-24 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-24}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{24}{5} & & \\ & V = \left\{ \frac{24}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-6x-1)& = & -3 \color{red}{+} (-3+x) \\\Leftrightarrow & -12x-2& = &-3-3+x \\\Leftrightarrow & -12x \color{red}{-2} & = &-6 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & -12x-x& = &-6+2 \\\Leftrightarrow & -13x& = &-4 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-4}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{4}{13} & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-x-3)& = & 6 \color{red}{+} (5+x) \\\Leftrightarrow & -6x-18& = &6+5+x \\\Leftrightarrow & -6x \color{red}{-18} & = &11 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & -6x-x& = &11+18 \\\Leftrightarrow & -7x& = &29 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{29}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-29}{7} & & \\ & V = \left\{ \frac{-29}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (4x+5)& = & 2 \color{red}{-} (12+x) \\\Leftrightarrow & 24x+30& = &2-12-x \\\Leftrightarrow & 24x \color{red}{+30} & = &-10 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & 24x+x& = &-10-30 \\\Leftrightarrow & 25x& = &-40 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-40}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-8}{5} & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)