Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{-7}& = & -8 \color{red}{ +4x } \\\Leftrightarrow & -x \color{red}{-7}\color{blue}{+7-4x } & = & -8 \color{red}{ +4x }\color{blue}{+7-4x } \\\Leftrightarrow & -x \color{blue}{-4x } & = & -8 \color{blue}{+7} \\\Leftrightarrow &-5x & = &-1\\\Leftrightarrow & \color{red}{-5}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{-3}& = & -13 \color{red}{ -15x } \\\Leftrightarrow & -x \color{red}{-3}\color{blue}{+3+15x } & = & -13 \color{red}{ -15x }\color{blue}{+3+15x } \\\Leftrightarrow & -x \color{blue}{+15x } & = & -13 \color{blue}{+3} \\\Leftrightarrow &14x & = &-10\\\Leftrightarrow & \color{red}{14}x & = &-10\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-10}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{+1}& = & 11 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{+1}\color{blue}{-1-9x } & = & 11 \color{red}{ +9x }\color{blue}{-1-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & 11 \color{blue}{-1} \\\Leftrightarrow &5x & = &10\\\Leftrightarrow & \color{red}{5}x & = &10\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{10}{5} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{+3}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+3}\color{blue}{-3-x } & = & -5 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -5 \color{blue}{-3} \\\Leftrightarrow &-11x & = &-8\\\Leftrightarrow & \color{red}{-11}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{8}{11} } & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{-10}& = & 15 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{-10}\color{blue}{+10+5x } & = & 15 \color{red}{ -5x }\color{blue}{+10+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & 15 \color{blue}{+10} \\\Leftrightarrow &16x & = &25\\\Leftrightarrow & \color{red}{16}x & = &25\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{25}{16} \\\Leftrightarrow & \color{green}{ x = \frac{25}{16} } & & \\ & V = \left\{ \frac{25}{16} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{+6}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+6}\color{blue}{-6-x } & = & -2 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -2 \color{blue}{-6} \\\Leftrightarrow &-3x & = &-8\\\Leftrightarrow & \color{red}{-3}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{-15}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-15}\color{blue}{+15-x } & = & -1 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -1 \color{blue}{+15} \\\Leftrightarrow &-11x & = &14\\\Leftrightarrow & \color{red}{-11}x & = &14\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{14}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{11} } & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{+15}& = & 2 \color{red}{ +2x } \\\Leftrightarrow & 5x \color{red}{+15}\color{blue}{-15-2x } & = & 2 \color{red}{ +2x }\color{blue}{-15-2x } \\\Leftrightarrow & 5x \color{blue}{-2x } & = & 2 \color{blue}{-15} \\\Leftrightarrow &3x & = &-13\\\Leftrightarrow & \color{red}{3}x & = &-13\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-13}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{3} } & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{+8}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+8}\color{blue}{-8-x } & = & 3 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 3 \color{blue}{-8} \\\Leftrightarrow &-3x & = &-5\\\Leftrightarrow & \color{red}{-3}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-5}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{-3}& = & 2 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-3}\color{blue}{+3-13x } & = & 2 \color{red}{ +13x }\color{blue}{+3-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 2 \color{blue}{+3} \\\Leftrightarrow &-25x & = &5\\\Leftrightarrow & \color{red}{-25}x & = &5\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{5}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{-3}& = & 9 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{-3}\color{blue}{+3-5x } & = & 9 \color{red}{ +5x }\color{blue}{+3-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & 9 \color{blue}{+3} \\\Leftrightarrow &-17x & = &12\\\Leftrightarrow & \color{red}{-17}x & = &12\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{12}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{17} } & & \\ & V = \left\{ \frac{-12}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{-6}& = & -11 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{-6}\color{blue}{+6-4x } & = & -11 \color{red}{ +4x }\color{blue}{+6-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & -11 \color{blue}{+6} \\\Leftrightarrow &-19x & = &-5\\\Leftrightarrow & \color{red}{-19}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-5}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{5}{19} } & & \\ & V = \left\{ \frac{5}{19} \right\} & \\\end{align}\)