Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-4x+4)& = & -13 \color{red}{+} (-11+x) \\\Leftrightarrow & -8x+8& = &-13-11+x \\\Leftrightarrow & -8x \color{red}{+8} & = &-24 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-24 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -8x-x& = &-24-8 \\\Leftrightarrow & -9x& = &-32 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-32}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{32}{9} & & \\ & V = \left\{ \frac{32}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (5x-2)& = & 6 \color{red}{-} (-14+x) \\\Leftrightarrow & 30x-12& = &6+14-x \\\Leftrightarrow & 30x \color{red}{-12} & = &20 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 30x+x& = &20+12 \\\Leftrightarrow & 31x& = &32 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{32}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{32}{31} & & \\ & V = \left\{ \frac{32}{31} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-5x-7)& = & 13 \color{red}{+} (5+x) \\\Leftrightarrow & -30x-42& = &13+5+x \\\Leftrightarrow & -30x \color{red}{-42} & = &18 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &18 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & -30x-x& = &18+42 \\\Leftrightarrow & -31x& = &60 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{60}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-60}{31} & & \\ & V = \left\{ \frac{-60}{31} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (2x+5)& = & -4 \color{red}{-} (-13+x) \\\Leftrightarrow & 10x+25& = &-4+13-x \\\Leftrightarrow & 10x \color{red}{+25} & = &9 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{+25} \color{blue}{-25} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{-25} \\\Leftrightarrow & 10x+x& = &9-25 \\\Leftrightarrow & 11x& = &-16 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-16}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-16}{11} & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (3x+5)& = & -4 \color{red}{+} (-5-2x) \\\Leftrightarrow & 15x+25& = &-4-5-2x \\\Leftrightarrow & 15x \color{red}{+25} & = &-9 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{+25} \color{blue}{-25} \color{blue}{+2x} & = &-9 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-25} \\\Leftrightarrow & 15x+2x& = &-9-25 \\\Leftrightarrow & 17x& = &-34 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-34}{ \color{red}{17} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (2x+6)& = & 2 \color{red}{+} (3+x) \\\Leftrightarrow & 4x+12& = &2+3+x \\\Leftrightarrow & 4x \color{red}{+12} & = &5 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 4x-x& = &5-12 \\\Leftrightarrow & 3x& = &-7 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-7}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-7}{3} & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-6x+4)& = & -5 \color{red}{+} (-6+x) \\\Leftrightarrow & -30x+20& = &-5-6+x \\\Leftrightarrow & -30x \color{red}{+20} & = &-11 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & -30x-x& = &-11-20 \\\Leftrightarrow & -31x& = &-31 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-31}{ \color{red}{-31} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (3x+3)& = & -15 \color{red}{-} (-8+x) \\\Leftrightarrow & 6x+6& = &-15+8-x \\\Leftrightarrow & 6x \color{red}{+6} & = &-7 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 6x+x& = &-7-6 \\\Leftrightarrow & 7x& = &-13 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-13}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-13}{7} & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (2x-2)& = & -10 \color{red}{-} (-7-5x) \\\Leftrightarrow & 6x-6& = &-10+7+5x \\\Leftrightarrow & 6x \color{red}{-6} & = &-3 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-6} \color{blue}{+6} \color{blue}{-5x} & = &-3 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+6} \\\Leftrightarrow & 6x-5x& = &-3+6 \\\Leftrightarrow & x& = &3 \\ & V = \left\{ 3 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-5x-6)& = & -4 \color{red}{+} (-7+4x) \\\Leftrightarrow & -25x-30& = &-4-7+4x \\\Leftrightarrow & -25x \color{red}{-30} & = &-11 \color{red}{+4x} \\\Leftrightarrow & -25x \color{red}{-30} \color{blue}{+30} \color{blue}{-4x} & = &-11 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+30} \\\Leftrightarrow & -25x-4x& = &-11+30 \\\Leftrightarrow & -29x& = &19 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{19}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-19}{29} & & \\ & V = \left\{ \frac{-19}{29} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-3x-4)& = & -6 \color{red}{+} (6+x) \\\Leftrightarrow & -9x-12& = &-6+6+x \\\Leftrightarrow & -9x \color{red}{-12} & = &0 \color{red}{+x} \\\Leftrightarrow & -9x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -9x-x& = &0+12 \\\Leftrightarrow & -10x& = &12 \\\Leftrightarrow & \frac{-10x}{ \color{red}{-10} }& = &\frac{12}{ \color{red}{-10} } \\\Leftrightarrow & x = \frac{-6}{5} & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-6x-4)& = & 15 \color{red}{-} (-3-5x) \\\Leftrightarrow & -36x-24& = &15+3+5x \\\Leftrightarrow & -36x \color{red}{-24} & = &18 \color{red}{+5x} \\\Leftrightarrow & -36x \color{red}{-24} \color{blue}{+24} \color{blue}{-5x} & = &18 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+24} \\\Leftrightarrow & -36x-5x& = &18+24 \\\Leftrightarrow & -41x& = &42 \\\Leftrightarrow & \frac{-41x}{ \color{red}{-41} }& = &\frac{42}{ \color{red}{-41} } \\\Leftrightarrow & x = \frac{-42}{41} & & \\ & V = \left\{ \frac{-42}{41} \right\} & \\\end{align}\)