Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-6x-6)& = & -15 \color{red}{-} (-11+x) \\\Leftrightarrow & -12x-12& = &-15+11-x \\\Leftrightarrow & -12x \color{red}{-12} & = &-4 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -12x+x& = &-4+12 \\\Leftrightarrow & -11x& = &8 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{8}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-8}{11} & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (3x-7)& = & 5 \color{red}{-} (7-4x) \\\Leftrightarrow & 9x-21& = &5-7+4x \\\Leftrightarrow & 9x \color{red}{-21} & = &-2 \color{red}{+4x} \\\Leftrightarrow & 9x \color{red}{-21} \color{blue}{+21} \color{blue}{-4x} & = &-2 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+21} \\\Leftrightarrow & 9x-4x& = &-2+21 \\\Leftrightarrow & 5x& = &19 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{19}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{19}{5} & & \\ & V = \left\{ \frac{19}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-6x-7)& = & 11 \color{red}{-} (-10+x) \\\Leftrightarrow & -12x-14& = &11+10-x \\\Leftrightarrow & -12x \color{red}{-14} & = &21 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &21 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & -12x+x& = &21+14 \\\Leftrightarrow & -11x& = &35 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{35}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-35}{11} & & \\ & V = \left\{ \frac{-35}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-5x+6)& = & -5 \color{red}{-} (7+x) \\\Leftrightarrow & -20x+24& = &-5-7-x \\\Leftrightarrow & -20x \color{red}{+24} & = &-12 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -20x+x& = &-12-24 \\\Leftrightarrow & -19x& = &-36 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-36}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{36}{19} & & \\ & V = \left\{ \frac{36}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (5x+4)& = & 6 \color{red}{-} (-5+x) \\\Leftrightarrow & 20x+16& = &6+5-x \\\Leftrightarrow & 20x \color{red}{+16} & = &11 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & 20x+x& = &11-16 \\\Leftrightarrow & 21x& = &-5 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-5}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-5}{21} & & \\ & V = \left\{ \frac{-5}{21} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (3x+1)& = & -1 \color{red}{+} (-4-5x) \\\Leftrightarrow & 18x+6& = &-1-4-5x \\\Leftrightarrow & 18x \color{red}{+6} & = &-5 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &-5 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & 18x+5x& = &-5-6 \\\Leftrightarrow & 23x& = &-11 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-11}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-11}{23} & & \\ & V = \left\{ \frac{-11}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-3x-6)& = & -11 \color{red}{+} (-4+x) \\\Leftrightarrow & -12x-24& = &-11-4+x \\\Leftrightarrow & -12x \color{red}{-24} & = &-15 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -12x-x& = &-15+24 \\\Leftrightarrow & -13x& = &9 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{9}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-9}{13} & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (6x+4)& = & 14 \color{red}{-} (-9-5x) \\\Leftrightarrow & 36x+24& = &14+9+5x \\\Leftrightarrow & 36x \color{red}{+24} & = &23 \color{red}{+5x} \\\Leftrightarrow & 36x \color{red}{+24} \color{blue}{-24} \color{blue}{-5x} & = &23 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-24} \\\Leftrightarrow & 36x-5x& = &23-24 \\\Leftrightarrow & 31x& = &-1 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-1}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-1}{31} & & \\ & V = \left\{ \frac{-1}{31} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (3x-5)& = & 5 \color{red}{+} (-3-2x) \\\Leftrightarrow & 9x-15& = &5-3-2x \\\Leftrightarrow & 9x \color{red}{-15} & = &2 \color{red}{-2x} \\\Leftrightarrow & 9x \color{red}{-15} \color{blue}{+15} \color{blue}{+2x} & = &2 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+15} \\\Leftrightarrow & 9x+2x& = &2+15 \\\Leftrightarrow & 11x& = &17 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{17}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{17}{11} & & \\ & V = \left\{ \frac{17}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (2x+6)& = & 7 \color{red}{+} (4-5x) \\\Leftrightarrow & 8x+24& = &7+4-5x \\\Leftrightarrow & 8x \color{red}{+24} & = &11 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{+24} \color{blue}{-24} \color{blue}{+5x} & = &11 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-24} \\\Leftrightarrow & 8x+5x& = &11-24 \\\Leftrightarrow & 13x& = &-13 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-13}{ \color{red}{13} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-2x+2)& = & -15 \color{red}{+} (6+x) \\\Leftrightarrow & -12x+12& = &-15+6+x \\\Leftrightarrow & -12x \color{red}{+12} & = &-9 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -12x-x& = &-9-12 \\\Leftrightarrow & -13x& = &-21 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-21}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{21}{13} & & \\ & V = \left\{ \frac{21}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (4x+1)& = & 12 \color{red}{-} (-10+3x) \\\Leftrightarrow & 16x+4& = &12+10-3x \\\Leftrightarrow & 16x \color{red}{+4} & = &22 \color{red}{-3x} \\\Leftrightarrow & 16x \color{red}{+4} \color{blue}{-4} \color{blue}{+3x} & = &22 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-4} \\\Leftrightarrow & 16x+3x& = &22-4 \\\Leftrightarrow & 19x& = &18 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{18}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{18}{19} & & \\ & V = \left\{ \frac{18}{19} \right\} & \\\end{align}\)