Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (4x-2)& = & -2 \color{red}{+} (12-5x) \\\Leftrightarrow & 16x-8& = &-2+12-5x \\\Leftrightarrow & 16x \color{red}{-8} & = &10 \color{red}{-5x} \\\Leftrightarrow & 16x \color{red}{-8} \color{blue}{+8} \color{blue}{+5x} & = &10 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+8} \\\Leftrightarrow & 16x+5x& = &10+8 \\\Leftrightarrow & 21x& = &18 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{18}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{6}{7} & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-2x+5)& = & 1 \color{red}{-} (14-5x) \\\Leftrightarrow & -8x+20& = &1-14+5x \\\Leftrightarrow & -8x \color{red}{+20} & = &-13 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{+20} \color{blue}{-20} \color{blue}{-5x} & = &-13 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-20} \\\Leftrightarrow & -8x-5x& = &-13-20 \\\Leftrightarrow & -13x& = &-33 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-33}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{33}{13} & & \\ & V = \left\{ \frac{33}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (3x-2)& = & 15 \color{red}{-} (-14+x) \\\Leftrightarrow & 12x-8& = &15+14-x \\\Leftrightarrow & 12x \color{red}{-8} & = &29 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &29 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 12x+x& = &29+8 \\\Leftrightarrow & 13x& = &37 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{37}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{37}{13} & & \\ & V = \left\{ \frac{37}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (3x-4)& = & 10 \color{red}{+} (-4+x) \\\Leftrightarrow & 9x-12& = &10-4+x \\\Leftrightarrow & 9x \color{red}{-12} & = &6 \color{red}{+x} \\\Leftrightarrow & 9x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 9x-x& = &6+12 \\\Leftrightarrow & 8x& = &18 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{18}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{9}{4} & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-2x+7)& = & 15 \color{red}{-} (-6+x) \\\Leftrightarrow & -12x+42& = &15+6-x \\\Leftrightarrow & -12x \color{red}{+42} & = &21 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &21 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & -12x+x& = &21-42 \\\Leftrightarrow & -11x& = &-21 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-21}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{21}{11} & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (4x+3)& = & 1 \color{red}{-} (7+x) \\\Leftrightarrow & 12x+9& = &1-7-x \\\Leftrightarrow & 12x \color{red}{+9} & = &-6 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+9} \color{blue}{-9} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{-9} \\\Leftrightarrow & 12x+x& = &-6-9 \\\Leftrightarrow & 13x& = &-15 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-15}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-15}{13} & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (4x+5)& = & -5 \color{red}{+} (-5+x) \\\Leftrightarrow & 8x+10& = &-5-5+x \\\Leftrightarrow & 8x \color{red}{+10} & = &-10 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & 8x-x& = &-10-10 \\\Leftrightarrow & 7x& = &-20 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-20}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-20}{7} & & \\ & V = \left\{ \frac{-20}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-2x-7)& = & -4 \color{red}{+} (14-5x) \\\Leftrightarrow & -6x-21& = &-4+14-5x \\\Leftrightarrow & -6x \color{red}{-21} & = &10 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-21} \color{blue}{+21} \color{blue}{+5x} & = &10 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+21} \\\Leftrightarrow & -6x+5x& = &10+21 \\\Leftrightarrow & -x& = &31 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{31}{ \color{red}{-1} } \\\Leftrightarrow & x = -31 & & \\ & V = \left\{ -31 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (5x+5)& = & 2 \color{red}{+} (-10+x) \\\Leftrightarrow & 15x+15& = &2-10+x \\\Leftrightarrow & 15x \color{red}{+15} & = &-8 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & 15x-x& = &-8-15 \\\Leftrightarrow & 14x& = &-23 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{-23}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{-23}{14} & & \\ & V = \left\{ \frac{-23}{14} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (x-3)& = & -7 \color{red}{+} (-12+x) \\\Leftrightarrow & 4x-12& = &-7-12+x \\\Leftrightarrow & 4x \color{red}{-12} & = &-19 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 4x-x& = &-19+12 \\\Leftrightarrow & 3x& = &-7 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-7}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-7}{3} & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (3x+5)& = & -5 \color{red}{+} (-4-2x) \\\Leftrightarrow & 9x+15& = &-5-4-2x \\\Leftrightarrow & 9x \color{red}{+15} & = &-9 \color{red}{-2x} \\\Leftrightarrow & 9x \color{red}{+15} \color{blue}{-15} \color{blue}{+2x} & = &-9 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-15} \\\Leftrightarrow & 9x+2x& = &-9-15 \\\Leftrightarrow & 11x& = &-24 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-24}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-24}{11} & & \\ & V = \left\{ \frac{-24}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-6x+5)& = & 13 \color{red}{+} (2+x) \\\Leftrightarrow & -24x+20& = &13+2+x \\\Leftrightarrow & -24x \color{red}{+20} & = &15 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & -24x-x& = &15-20 \\\Leftrightarrow & -25x& = &-5 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-5}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{1}{5} & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)