Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (6x+1)& = & 3 \color{red}{-} (-15+x) \\\Leftrightarrow & 24x+4& = &3+15-x \\\Leftrightarrow & 24x \color{red}{+4} & = &18 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &18 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 24x+x& = &18-4 \\\Leftrightarrow & 25x& = &14 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{14}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{14}{25} & & \\ & V = \left\{ \frac{14}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (3x-1)& = & -3 \color{red}{+} (-6+x) \\\Leftrightarrow & 18x-6& = &-3-6+x \\\Leftrightarrow & 18x \color{red}{-6} & = &-9 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 18x-x& = &-9+6 \\\Leftrightarrow & 17x& = &-3 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-3}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-3}{17} & & \\ & V = \left\{ \frac{-3}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-5x+4)& = & -7 \color{red}{+} (3+x) \\\Leftrightarrow & -20x+16& = &-7+3+x \\\Leftrightarrow & -20x \color{red}{+16} & = &-4 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & -20x-x& = &-4-16 \\\Leftrightarrow & -21x& = &-20 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-20}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{20}{21} & & \\ & V = \left\{ \frac{20}{21} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-5x+2)& = & -2 \color{red}{+} (7+x) \\\Leftrightarrow & -20x+8& = &-2+7+x \\\Leftrightarrow & -20x \color{red}{+8} & = &5 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -20x-x& = &5-8 \\\Leftrightarrow & -21x& = &-3 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-3}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{1}{7} & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-3x+3)& = & -9 \color{red}{+} (12+2x) \\\Leftrightarrow & -9x+9& = &-9+12+2x \\\Leftrightarrow & -9x \color{red}{+9} & = &3 \color{red}{+2x} \\\Leftrightarrow & -9x \color{red}{+9} \color{blue}{-9} \color{blue}{-2x} & = &3 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-9} \\\Leftrightarrow & -9x-2x& = &3-9 \\\Leftrightarrow & -11x& = &-6 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-6}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{6}{11} & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-6x+1)& = & -1 \color{red}{+} (12+x) \\\Leftrightarrow & -18x+3& = &-1+12+x \\\Leftrightarrow & -18x \color{red}{+3} & = &11 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & -18x-x& = &11-3 \\\Leftrightarrow & -19x& = &8 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{8}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-8}{19} & & \\ & V = \left\{ \frac{-8}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-6x-4)& = & -15 \color{red}{+} (1+x) \\\Leftrightarrow & -12x-8& = &-15+1+x \\\Leftrightarrow & -12x \color{red}{-8} & = &-14 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -12x-x& = &-14+8 \\\Leftrightarrow & -13x& = &-6 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-6}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{6}{13} & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-5x-3)& = & 13 \color{red}{-} (3+x) \\\Leftrightarrow & -15x-9& = &13-3-x \\\Leftrightarrow & -15x \color{red}{-9} & = &10 \color{red}{-x} \\\Leftrightarrow & -15x \color{red}{-9} \color{blue}{+9} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{+9} \\\Leftrightarrow & -15x+x& = &10+9 \\\Leftrightarrow & -14x& = &19 \\\Leftrightarrow & \frac{-14x}{ \color{red}{-14} }& = &\frac{19}{ \color{red}{-14} } \\\Leftrightarrow & x = \frac{-19}{14} & & \\ & V = \left\{ \frac{-19}{14} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (3x+1)& = & 13 \color{red}{+} (4+4x) \\\Leftrightarrow & 15x+5& = &13+4+4x \\\Leftrightarrow & 15x \color{red}{+5} & = &17 \color{red}{+4x} \\\Leftrightarrow & 15x \color{red}{+5} \color{blue}{-5} \color{blue}{-4x} & = &17 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-5} \\\Leftrightarrow & 15x-4x& = &17-5 \\\Leftrightarrow & 11x& = &12 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{12}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{12}{11} & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (5x+1)& = & 1 \color{red}{+} (6+x) \\\Leftrightarrow & 30x+6& = &1+6+x \\\Leftrightarrow & 30x \color{red}{+6} & = &7 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 30x-x& = &7-6 \\\Leftrightarrow & 29x& = &1 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{1}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{1}{29} & & \\ & V = \left\{ \frac{1}{29} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-4x-1)& = & 7 \color{red}{+} (-10+3x) \\\Leftrightarrow & -20x-5& = &7-10+3x \\\Leftrightarrow & -20x \color{red}{-5} & = &-3 \color{red}{+3x} \\\Leftrightarrow & -20x \color{red}{-5} \color{blue}{+5} \color{blue}{-3x} & = &-3 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+5} \\\Leftrightarrow & -20x-3x& = &-3+5 \\\Leftrightarrow & -23x& = &2 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{2}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-2}{23} & & \\ & V = \left\{ \frac{-2}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (x-3)& = & 14 \color{red}{+} (1-5x) \\\Leftrightarrow & 3x-9& = &14+1-5x \\\Leftrightarrow & 3x \color{red}{-9} & = &15 \color{red}{-5x} \\\Leftrightarrow & 3x \color{red}{-9} \color{blue}{+9} \color{blue}{+5x} & = &15 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+9} \\\Leftrightarrow & 3x+5x& = &15+9 \\\Leftrightarrow & 8x& = &24 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{24}{ \color{red}{8} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)