Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-3x-1)& = & 1 \color{red}{-} (13+x) \\\Leftrightarrow & -18x-6& = &1-13-x \\\Leftrightarrow & -18x \color{red}{-6} & = &-12 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -18x+x& = &-12+6 \\\Leftrightarrow & -17x& = &-6 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-6}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{6}{17} & & \\ & V = \left\{ \frac{6}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-2x-7)& = & 4 \color{red}{+} (2+x) \\\Leftrightarrow & -10x-35& = &4+2+x \\\Leftrightarrow & -10x \color{red}{-35} & = &6 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{-35} \color{blue}{+35} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{+35} \\\Leftrightarrow & -10x-x& = &6+35 \\\Leftrightarrow & -11x& = &41 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{41}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-41}{11} & & \\ & V = \left\{ \frac{-41}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (3x-6)& = & -11 \color{red}{-} (3-4x) \\\Leftrightarrow & 9x-18& = &-11-3+4x \\\Leftrightarrow & 9x \color{red}{-18} & = &-14 \color{red}{+4x} \\\Leftrightarrow & 9x \color{red}{-18} \color{blue}{+18} \color{blue}{-4x} & = &-14 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+18} \\\Leftrightarrow & 9x-4x& = &-14+18 \\\Leftrightarrow & 5x& = &4 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{4}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{4}{5} & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (4x-1)& = & -2 \color{red}{+} (7+x) \\\Leftrightarrow & 12x-3& = &-2+7+x \\\Leftrightarrow & 12x \color{red}{-3} & = &5 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & 12x-x& = &5+3 \\\Leftrightarrow & 11x& = &8 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{8}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{8}{11} & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (3x+7)& = & -10 \color{red}{+} (-2+x) \\\Leftrightarrow & 9x+21& = &-10-2+x \\\Leftrightarrow & 9x \color{red}{+21} & = &-12 \color{red}{+x} \\\Leftrightarrow & 9x \color{red}{+21} \color{blue}{-21} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{-21} \\\Leftrightarrow & 9x-x& = &-12-21 \\\Leftrightarrow & 8x& = &-33 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{-33}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{-33}{8} & & \\ & V = \left\{ \frac{-33}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (5x+4)& = & 15 \color{red}{+} (8+x) \\\Leftrightarrow & 10x+8& = &15+8+x \\\Leftrightarrow & 10x \color{red}{+8} & = &23 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &23 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 10x-x& = &23-8 \\\Leftrightarrow & 9x& = &15 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{15}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{5}{3} & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-6x-6)& = & 14 \color{red}{+} (-6+x) \\\Leftrightarrow & -24x-24& = &14-6+x \\\Leftrightarrow & -24x \color{red}{-24} & = &8 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -24x-x& = &8+24 \\\Leftrightarrow & -25x& = &32 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{32}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-32}{25} & & \\ & V = \left\{ \frac{-32}{25} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-4x+1)& = & -5 \color{red}{+} (-12+3x) \\\Leftrightarrow & -20x+5& = &-5-12+3x \\\Leftrightarrow & -20x \color{red}{+5} & = &-17 \color{red}{+3x} \\\Leftrightarrow & -20x \color{red}{+5} \color{blue}{-5} \color{blue}{-3x} & = &-17 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-5} \\\Leftrightarrow & -20x-3x& = &-17-5 \\\Leftrightarrow & -23x& = &-22 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-22}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{22}{23} & & \\ & V = \left\{ \frac{22}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (x-7)& = & -14 \color{red}{+} (1-3x) \\\Leftrightarrow & 4x-28& = &-14+1-3x \\\Leftrightarrow & 4x \color{red}{-28} & = &-13 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-28} \color{blue}{+28} \color{blue}{+3x} & = &-13 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+28} \\\Leftrightarrow & 4x+3x& = &-13+28 \\\Leftrightarrow & 7x& = &15 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{15}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{15}{7} & & \\ & V = \left\{ \frac{15}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (2x-1)& = & -14 \color{red}{+} (-2-3x) \\\Leftrightarrow & 4x-2& = &-14-2-3x \\\Leftrightarrow & 4x \color{red}{-2} & = &-16 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-2} \color{blue}{+2} \color{blue}{+3x} & = &-16 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+2} \\\Leftrightarrow & 4x+3x& = &-16+2 \\\Leftrightarrow & 7x& = &-14 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-14}{ \color{red}{7} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-4x+4)& = & 4 \color{red}{-} (2+x) \\\Leftrightarrow & -12x+12& = &4-2-x \\\Leftrightarrow & -12x \color{red}{+12} & = &2 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -12x+x& = &2-12 \\\Leftrightarrow & -11x& = &-10 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-10}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{10}{11} & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (3x+2)& = & -12 \color{red}{-} (9-2x) \\\Leftrightarrow & 9x+6& = &-12-9+2x \\\Leftrightarrow & 9x \color{red}{+6} & = &-21 \color{red}{+2x} \\\Leftrightarrow & 9x \color{red}{+6} \color{blue}{-6} \color{blue}{-2x} & = &-21 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-6} \\\Leftrightarrow & 9x-2x& = &-21-6 \\\Leftrightarrow & 7x& = &-27 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-27}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-27}{7} & & \\ & V = \left\{ \frac{-27}{7} \right\} & \\\end{align}\)