Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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