Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (3x+7)& = & -4 \color{red}{+} (-14+x) \\\Leftrightarrow & 18x+42& = &-4-14+x \\\Leftrightarrow & 18x \color{red}{+42} & = &-18 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &-18 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & 18x-x& = &-18-42 \\\Leftrightarrow & 17x& = &-60 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-60}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-60}{17} & & \\ & V = \left\{ \frac{-60}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (3x+3)& = & 14 \color{red}{+} (9-5x) \\\Leftrightarrow & 6x+6& = &14+9-5x \\\Leftrightarrow & 6x \color{red}{+6} & = &23 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &23 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & 6x+5x& = &23-6 \\\Leftrightarrow & 11x& = &17 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{17}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{17}{11} & & \\ & V = \left\{ \frac{17}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (3x+7)& = & 8 \color{red}{-} (3+x) \\\Leftrightarrow & 15x+35& = &8-3-x \\\Leftrightarrow & 15x \color{red}{+35} & = &5 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{+35} \color{blue}{-35} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{-35} \\\Leftrightarrow & 15x+x& = &5-35 \\\Leftrightarrow & 16x& = &-30 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{-30}{ \color{red}{16} } \\\Leftrightarrow & x = \frac{-15}{8} & & \\ & V = \left\{ \frac{-15}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (2x-7)& = & 1 \color{red}{+} (4+x) \\\Leftrightarrow & 12x-42& = &1+4+x \\\Leftrightarrow & 12x \color{red}{-42} & = &5 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & 12x-x& = &5+42 \\\Leftrightarrow & 11x& = &47 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{47}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{47}{11} & & \\ & V = \left\{ \frac{47}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-2x-7)& = & 11 \color{red}{-} (1+x) \\\Leftrightarrow & -8x-28& = &11-1-x \\\Leftrightarrow & -8x \color{red}{-28} & = &10 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & -8x+x& = &10+28 \\\Leftrightarrow & -7x& = &38 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{38}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-38}{7} & & \\ & V = \left\{ \frac{-38}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-5x-3)& = & 5 \color{red}{+} (-10-3x) \\\Leftrightarrow & -25x-15& = &5-10-3x \\\Leftrightarrow & -25x \color{red}{-15} & = &-5 \color{red}{-3x} \\\Leftrightarrow & -25x \color{red}{-15} \color{blue}{+15} \color{blue}{+3x} & = &-5 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+15} \\\Leftrightarrow & -25x+3x& = &-5+15 \\\Leftrightarrow & -22x& = &10 \\\Leftrightarrow & \frac{-22x}{ \color{red}{-22} }& = &\frac{10}{ \color{red}{-22} } \\\Leftrightarrow & x = \frac{-5}{11} & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-6x+7)& = & 1 \color{red}{-} (-10-5x) \\\Leftrightarrow & -18x+21& = &1+10+5x \\\Leftrightarrow & -18x \color{red}{+21} & = &11 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+21} \color{blue}{-21} \color{blue}{-5x} & = &11 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-21} \\\Leftrightarrow & -18x-5x& = &11-21 \\\Leftrightarrow & -23x& = &-10 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-10}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{10}{23} & & \\ & V = \left\{ \frac{10}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (2x-6)& = & 9 \color{red}{-} (12+x) \\\Leftrightarrow & 4x-12& = &9-12-x \\\Leftrightarrow & 4x \color{red}{-12} & = &-3 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 4x+x& = &-3+12 \\\Leftrightarrow & 5x& = &9 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{9}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{9}{5} & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (x+3)& = & 4 \color{red}{+} (15-4x) \\\Leftrightarrow & 5x+15& = &4+15-4x \\\Leftrightarrow & 5x \color{red}{+15} & = &19 \color{red}{-4x} \\\Leftrightarrow & 5x \color{red}{+15} \color{blue}{-15} \color{blue}{+4x} & = &19 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-15} \\\Leftrightarrow & 5x+4x& = &19-15 \\\Leftrightarrow & 9x& = &4 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{4}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{4}{9} & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-5x-6)& = & -10 \color{red}{-} (-14-2x) \\\Leftrightarrow & -25x-30& = &-10+14+2x \\\Leftrightarrow & -25x \color{red}{-30} & = &4 \color{red}{+2x} \\\Leftrightarrow & -25x \color{red}{-30} \color{blue}{+30} \color{blue}{-2x} & = &4 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+30} \\\Leftrightarrow & -25x-2x& = &4+30 \\\Leftrightarrow & -27x& = &34 \\\Leftrightarrow & \frac{-27x}{ \color{red}{-27} }& = &\frac{34}{ \color{red}{-27} } \\\Leftrightarrow & x = \frac{-34}{27} & & \\ & V = \left\{ \frac{-34}{27} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-4x-4)& = & -10 \color{red}{-} (-12+x) \\\Leftrightarrow & -12x-12& = &-10+12-x \\\Leftrightarrow & -12x \color{red}{-12} & = &2 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -12x+x& = &2+12 \\\Leftrightarrow & -11x& = &14 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{14}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-14}{11} & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-2x+3)& = & 3 \color{red}{-} (14+x) \\\Leftrightarrow & -12x+18& = &3-14-x \\\Leftrightarrow & -12x \color{red}{+18} & = &-11 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -12x+x& = &-11-18 \\\Leftrightarrow & -11x& = &-29 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-29}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{29}{11} & & \\ & V = \left\{ \frac{29}{11} \right\} & \\\end{align}\)