Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (5x-2)& = & 3 \color{red}{+} (9+x) \\\Leftrightarrow & 30x-12& = &3+9+x \\\Leftrightarrow & 30x \color{red}{-12} & = &12 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 30x-x& = &12+12 \\\Leftrightarrow & 29x& = &24 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{24}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{24}{29} & & \\ & V = \left\{ \frac{24}{29} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (2x+5)& = & 15 \color{red}{+} (-13+x) \\\Leftrightarrow & 12x+30& = &15-13+x \\\Leftrightarrow & 12x \color{red}{+30} & = &2 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & 12x-x& = &2-30 \\\Leftrightarrow & 11x& = &-28 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-28}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-28}{11} & & \\ & V = \left\{ \frac{-28}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-5x-5)& = & -11 \color{red}{+} (-6+x) \\\Leftrightarrow & -20x-20& = &-11-6+x \\\Leftrightarrow & -20x \color{red}{-20} & = &-17 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & -20x-x& = &-17+20 \\\Leftrightarrow & -21x& = &3 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{3}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-1}{7} & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (3x-5)& = & 8 \color{red}{-} (-8-4x) \\\Leftrightarrow & 9x-15& = &8+8+4x \\\Leftrightarrow & 9x \color{red}{-15} & = &16 \color{red}{+4x} \\\Leftrightarrow & 9x \color{red}{-15} \color{blue}{+15} \color{blue}{-4x} & = &16 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+15} \\\Leftrightarrow & 9x-4x& = &16+15 \\\Leftrightarrow & 5x& = &31 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{31}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{31}{5} & & \\ & V = \left\{ \frac{31}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (6x-4)& = & 11 \color{red}{-} (6-5x) \\\Leftrightarrow & 18x-12& = &11-6+5x \\\Leftrightarrow & 18x \color{red}{-12} & = &5 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &5 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & 18x-5x& = &5+12 \\\Leftrightarrow & 13x& = &17 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{17}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{17}{13} & & \\ & V = \left\{ \frac{17}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-6x-5)& = & 4 \color{red}{-} (-3-5x) \\\Leftrightarrow & -36x-30& = &4+3+5x \\\Leftrightarrow & -36x \color{red}{-30} & = &7 \color{red}{+5x} \\\Leftrightarrow & -36x \color{red}{-30} \color{blue}{+30} \color{blue}{-5x} & = &7 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+30} \\\Leftrightarrow & -36x-5x& = &7+30 \\\Leftrightarrow & -41x& = &37 \\\Leftrightarrow & \frac{-41x}{ \color{red}{-41} }& = &\frac{37}{ \color{red}{-41} } \\\Leftrightarrow & x = \frac{-37}{41} & & \\ & V = \left\{ \frac{-37}{41} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-2x-7)& = & 11 \color{red}{+} (5+x) \\\Leftrightarrow & -12x-42& = &11+5+x \\\Leftrightarrow & -12x \color{red}{-42} & = &16 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & -12x-x& = &16+42 \\\Leftrightarrow & -13x& = &58 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{58}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-58}{13} & & \\ & V = \left\{ \frac{-58}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-4x+6)& = & -10 \color{red}{-} (2+x) \\\Leftrightarrow & -12x+18& = &-10-2-x \\\Leftrightarrow & -12x \color{red}{+18} & = &-12 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -12x+x& = &-12-18 \\\Leftrightarrow & -11x& = &-30 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-30}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{30}{11} & & \\ & V = \left\{ \frac{30}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-x-5)& = & -4 \color{red}{+} (6+4x) \\\Leftrightarrow & -5x-25& = &-4+6+4x \\\Leftrightarrow & -5x \color{red}{-25} & = &2 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{-25} \color{blue}{+25} \color{blue}{-4x} & = &2 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+25} \\\Leftrightarrow & -5x-4x& = &2+25 \\\Leftrightarrow & -9x& = &27 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{27}{ \color{red}{-9} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (4x-2)& = & 6 \color{red}{+} (-9+3x) \\\Leftrightarrow & 20x-10& = &6-9+3x \\\Leftrightarrow & 20x \color{red}{-10} & = &-3 \color{red}{+3x} \\\Leftrightarrow & 20x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &-3 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & 20x-3x& = &-3+10 \\\Leftrightarrow & 17x& = &7 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{7}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{7}{17} & & \\ & V = \left\{ \frac{7}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-3x-5)& = & 2 \color{red}{+} (-14-2x) \\\Leftrightarrow & -9x-15& = &2-14-2x \\\Leftrightarrow & -9x \color{red}{-15} & = &-12 \color{red}{-2x} \\\Leftrightarrow & -9x \color{red}{-15} \color{blue}{+15} \color{blue}{+2x} & = &-12 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+15} \\\Leftrightarrow & -9x+2x& = &-12+15 \\\Leftrightarrow & -7x& = &3 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{3}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-3}{7} & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (6x+4)& = & -3 \color{red}{-} (-10+x) \\\Leftrightarrow & 24x+16& = &-3+10-x \\\Leftrightarrow & 24x \color{red}{+16} & = &7 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & 24x+x& = &7-16 \\\Leftrightarrow & 25x& = &-9 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-9}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-9}{25} & & \\ & V = \left\{ \frac{-9}{25} \right\} & \\\end{align}\)