Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (5x+6)& = & -7 \color{red}{-} (-11+x) \\\Leftrightarrow & 30x+36& = &-7+11-x \\\Leftrightarrow & 30x \color{red}{+36} & = &4 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & 30x+x& = &4-36 \\\Leftrightarrow & 31x& = &-32 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-32}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-32}{31} & & \\ & V = \left\{ \frac{-32}{31} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (x+7)& = & 4 \color{red}{+} (8+3x) \\\Leftrightarrow & 2x+14& = &4+8+3x \\\Leftrightarrow & 2x \color{red}{+14} & = &12 \color{red}{+3x} \\\Leftrightarrow & 2x \color{red}{+14} \color{blue}{-14} \color{blue}{-3x} & = &12 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-14} \\\Leftrightarrow & 2x-3x& = &12-14 \\\Leftrightarrow & -x& = &-2 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-2}{ \color{red}{-1} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-4x-1)& = & 3 \color{red}{-} (5+x) \\\Leftrightarrow & -20x-5& = &3-5-x \\\Leftrightarrow & -20x \color{red}{-5} & = &-2 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-5} \color{blue}{+5} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+5} \\\Leftrightarrow & -20x+x& = &-2+5 \\\Leftrightarrow & -19x& = &3 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{3}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-3}{19} & & \\ & V = \left\{ \frac{-3}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-2x+4)& = & -10 \color{red}{+} (12+x) \\\Leftrightarrow & -6x+12& = &-10+12+x \\\Leftrightarrow & -6x \color{red}{+12} & = &2 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -6x-x& = &2-12 \\\Leftrightarrow & -7x& = &-10 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-10}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{10}{7} & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-6x+2)& = & 1 \color{red}{+} (-7+x) \\\Leftrightarrow & -30x+10& = &1-7+x \\\Leftrightarrow & -30x \color{red}{+10} & = &-6 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & -30x-x& = &-6-10 \\\Leftrightarrow & -31x& = &-16 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-16}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{16}{31} & & \\ & V = \left\{ \frac{16}{31} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-x-5)& = & -2 \color{red}{-} (4+x) \\\Leftrightarrow & -5x-25& = &-2-4-x \\\Leftrightarrow & -5x \color{red}{-25} & = &-6 \color{red}{-x} \\\Leftrightarrow & -5x \color{red}{-25} \color{blue}{+25} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+25} \\\Leftrightarrow & -5x+x& = &-6+25 \\\Leftrightarrow & -4x& = &19 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{19}{ \color{red}{-4} } \\\Leftrightarrow & x = \frac{-19}{4} & & \\ & V = \left\{ \frac{-19}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-3x+6)& = & 13 \color{red}{+} (9+x) \\\Leftrightarrow & -15x+30& = &13+9+x \\\Leftrightarrow & -15x \color{red}{+30} & = &22 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &22 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -15x-x& = &22-30 \\\Leftrightarrow & -16x& = &-8 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{-8}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{1}{2} & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (6x-5)& = & 14 \color{red}{+} (-10+x) \\\Leftrightarrow & 24x-20& = &14-10+x \\\Leftrightarrow & 24x \color{red}{-20} & = &4 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 24x-x& = &4+20 \\\Leftrightarrow & 23x& = &24 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{24}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{24}{23} & & \\ & V = \left\{ \frac{24}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (4x+1)& = & 9 \color{red}{-} (6+x) \\\Leftrightarrow & 8x+2& = &9-6-x \\\Leftrightarrow & 8x \color{red}{+2} & = &3 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & 8x+x& = &3-2 \\\Leftrightarrow & 9x& = &1 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{1}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{1}{9} & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-2x+2)& = & 1 \color{red}{-} (-13+x) \\\Leftrightarrow & -8x+8& = &1+13-x \\\Leftrightarrow & -8x \color{red}{+8} & = &14 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -8x+x& = &14-8 \\\Leftrightarrow & -7x& = &6 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{6}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-6}{7} & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (4x-4)& = & 13 \color{red}{-} (9+x) \\\Leftrightarrow & 24x-24& = &13-9-x \\\Leftrightarrow & 24x \color{red}{-24} & = &4 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 24x+x& = &4+24 \\\Leftrightarrow & 25x& = &28 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{28}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{28}{25} & & \\ & V = \left\{ \frac{28}{25} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-4x-4)& = & 10 \color{red}{-} (-14+x) \\\Leftrightarrow & -12x-12& = &10+14-x \\\Leftrightarrow & -12x \color{red}{-12} & = &24 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &24 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -12x+x& = &24+12 \\\Leftrightarrow & -11x& = &36 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{36}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-36}{11} & & \\ & V = \left\{ \frac{-36}{11} \right\} & \\\end{align}\)