Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-2x+4)& = & 2 \color{red}{+} (-15+x) \\\Leftrightarrow & -6x+12& = &2-15+x \\\Leftrightarrow & -6x \color{red}{+12} & = &-13 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -6x-x& = &-13-12 \\\Leftrightarrow & -7x& = &-25 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-25}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{25}{7} & & \\ & V = \left\{ \frac{25}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-x+4)& = & -4 \color{red}{-} (9-3x) \\\Leftrightarrow & -4x+16& = &-4-9+3x \\\Leftrightarrow & -4x \color{red}{+16} & = &-13 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+16} \color{blue}{-16} \color{blue}{-3x} & = &-13 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-16} \\\Leftrightarrow & -4x-3x& = &-13-16 \\\Leftrightarrow & -7x& = &-29 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-29}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{29}{7} & & \\ & V = \left\{ \frac{29}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-3x+4)& = & 8 \color{red}{-} (-6-4x) \\\Leftrightarrow & -9x+12& = &8+6+4x \\\Leftrightarrow & -9x \color{red}{+12} & = &14 \color{red}{+4x} \\\Leftrightarrow & -9x \color{red}{+12} \color{blue}{-12} \color{blue}{-4x} & = &14 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-12} \\\Leftrightarrow & -9x-4x& = &14-12 \\\Leftrightarrow & -13x& = &2 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{2}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-2}{13} & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-5x-1)& = & -7 \color{red}{-} (5+x) \\\Leftrightarrow & -30x-6& = &-7-5-x \\\Leftrightarrow & -30x \color{red}{-6} & = &-12 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -30x+x& = &-12+6 \\\Leftrightarrow & -29x& = &-6 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-6}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{6}{29} & & \\ & V = \left\{ \frac{6}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (5x-6)& = & 8 \color{red}{+} (-9+3x) \\\Leftrightarrow & 10x-12& = &8-9+3x \\\Leftrightarrow & 10x \color{red}{-12} & = &-1 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-12} \color{blue}{+12} \color{blue}{-3x} & = &-1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+12} \\\Leftrightarrow & 10x-3x& = &-1+12 \\\Leftrightarrow & 7x& = &11 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{11}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{11}{7} & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-6x-3)& = & -9 \color{red}{+} (5-5x) \\\Leftrightarrow & -36x-18& = &-9+5-5x \\\Leftrightarrow & -36x \color{red}{-18} & = &-4 \color{red}{-5x} \\\Leftrightarrow & -36x \color{red}{-18} \color{blue}{+18} \color{blue}{+5x} & = &-4 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+18} \\\Leftrightarrow & -36x+5x& = &-4+18 \\\Leftrightarrow & -31x& = &14 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{14}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-14}{31} & & \\ & V = \left\{ \frac{-14}{31} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-6x-5)& = & 15 \color{red}{+} (-10+x) \\\Leftrightarrow & -12x-10& = &15-10+x \\\Leftrightarrow & -12x \color{red}{-10} & = &5 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & -12x-x& = &5+10 \\\Leftrightarrow & -13x& = &15 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{15}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-15}{13} & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (2x+6)& = & 10 \color{red}{+} (-7+x) \\\Leftrightarrow & 12x+36& = &10-7+x \\\Leftrightarrow & 12x \color{red}{+36} & = &3 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & 12x-x& = &3-36 \\\Leftrightarrow & 11x& = &-33 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-33}{ \color{red}{11} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-2x+2)& = & 14 \color{red}{+} (-6+x) \\\Leftrightarrow & -8x+8& = &14-6+x \\\Leftrightarrow & -8x \color{red}{+8} & = &8 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -8x-x& = &8-8 \\\Leftrightarrow & -9x& = &0 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{0}{ \color{red}{-9} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (3x+3)& = & 14 \color{red}{-} (4-2x) \\\Leftrightarrow & 15x+15& = &14-4+2x \\\Leftrightarrow & 15x \color{red}{+15} & = &10 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+15} \color{blue}{-15} \color{blue}{-2x} & = &10 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-15} \\\Leftrightarrow & 15x-2x& = &10-15 \\\Leftrightarrow & 13x& = &-5 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-5}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-5}{13} & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (4x-5)& = & -4 \color{red}{+} (-4+x) \\\Leftrightarrow & 20x-25& = &-4-4+x \\\Leftrightarrow & 20x \color{red}{-25} & = &-8 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-25} \color{blue}{+25} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{+25} \\\Leftrightarrow & 20x-x& = &-8+25 \\\Leftrightarrow & 19x& = &17 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{17}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{17}{19} & & \\ & V = \left\{ \frac{17}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (4x-4)& = & -8 \color{red}{+} (5-5x) \\\Leftrightarrow & 16x-16& = &-8+5-5x \\\Leftrightarrow & 16x \color{red}{-16} & = &-3 \color{red}{-5x} \\\Leftrightarrow & 16x \color{red}{-16} \color{blue}{+16} \color{blue}{+5x} & = &-3 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+16} \\\Leftrightarrow & 16x+5x& = &-3+16 \\\Leftrightarrow & 21x& = &13 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{13}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{13}{21} & & \\ & V = \left\{ \frac{13}{21} \right\} & \\\end{align}\)