Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{-8}& = & -7 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-8}\color{blue}{+8-9x } & = & -7 \color{red}{ +9x }\color{blue}{+8-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & -7 \color{blue}{+8} \\\Leftrightarrow &-13x & = &1\\\Leftrightarrow & \color{red}{-13}x & = &1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{+2}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+2}\color{blue}{-2-x } & = & -8 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -8 \color{blue}{-2} \\\Leftrightarrow &-15x & = &-10\\\Leftrightarrow & \color{red}{-15}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-10}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{+5}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+5}\color{blue}{-5-x } & = & -9 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -9 \color{blue}{-5} \\\Leftrightarrow &-4x & = &-14\\\Leftrightarrow & \color{red}{-4}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-14}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{-11}& = & 12 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{-11}\color{blue}{+11+8x } & = & 12 \color{red}{ -8x }\color{blue}{+11+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & 12 \color{blue}{+11} \\\Leftrightarrow &17x & = &23\\\Leftrightarrow & \color{red}{17}x & = &23\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{23}{17} \\\Leftrightarrow & \color{green}{ x = \frac{23}{17} } & & \\ & V = \left\{ \frac{23}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{-7}& = & 8 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{-7}\color{blue}{+7-11x } & = & 8 \color{red}{ +11x }\color{blue}{+7-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & 8 \color{blue}{+7} \\\Leftrightarrow &-18x & = &15\\\Leftrightarrow & \color{red}{-18}x & = &15\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{15}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{-8}& = & -4 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{-8}\color{blue}{+8+4x } & = & -4 \color{red}{ -4x }\color{blue}{+8+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -4 \color{blue}{+8} \\\Leftrightarrow &13x & = &4\\\Leftrightarrow & \color{red}{13}x & = &4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{-6}& = & 1 \color{red}{ -7x } \\\Leftrightarrow & 5x \color{red}{-6}\color{blue}{+6+7x } & = & 1 \color{red}{ -7x }\color{blue}{+6+7x } \\\Leftrightarrow & 5x \color{blue}{+7x } & = & 1 \color{blue}{+6} \\\Leftrightarrow &12x & = &7\\\Leftrightarrow & \color{red}{12}x & = &7\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{7}{12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{12} } & & \\ & V = \left\{ \frac{7}{12} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{-3}& = & -15 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-3}\color{blue}{+3+8x } & = & -15 \color{red}{ -8x }\color{blue}{+3+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & -15 \color{blue}{+3} \\\Leftrightarrow &11x & = &-12\\\Leftrightarrow & \color{red}{11}x & = &-12\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-12}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{11} } & & \\ & V = \left\{ \frac{-12}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{-4}& = & 12 \color{red}{ +8x } \\\Leftrightarrow & 5x \color{red}{-4}\color{blue}{+4-8x } & = & 12 \color{red}{ +8x }\color{blue}{+4-8x } \\\Leftrightarrow & 5x \color{blue}{-8x } & = & 12 \color{blue}{+4} \\\Leftrightarrow &-3x & = &16\\\Leftrightarrow & \color{red}{-3}x & = &16\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{16}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{3} } & & \\ & V = \left\{ \frac{-16}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{+6}& = & 5 \color{red}{ +8x } \\\Leftrightarrow & 5x \color{red}{+6}\color{blue}{-6-8x } & = & 5 \color{red}{ +8x }\color{blue}{-6-8x } \\\Leftrightarrow & 5x \color{blue}{-8x } & = & 5 \color{blue}{-6} \\\Leftrightarrow &-3x & = &-1\\\Leftrightarrow & \color{red}{-3}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 2x \color{red}{+1}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+1}\color{blue}{-1-x } & = & 3 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 3 \color{blue}{-1} \\\Leftrightarrow &x & = &2\\\Leftrightarrow & \color{red}{}x & = &2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 2 \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{-4}& = & 11 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{-4}\color{blue}{+4-8x } & = & 11 \color{red}{ +8x }\color{blue}{+4-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & 11 \color{blue}{+4} \\\Leftrightarrow &-23x & = &15\\\Leftrightarrow & \color{red}{-23}x & = &15\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{15}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{23} } & & \\ & V = \left\{ \frac{-15}{23} \right\} & \\\end{align}\)