Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{-10}& = & 5 \color{red}{ +9x } \\\Leftrightarrow & 10x \color{red}{-10}\color{blue}{+10-9x } & = & 5 \color{red}{ +9x }\color{blue}{+10-9x } \\\Leftrightarrow & 10x \color{blue}{-9x } & = & 5 \color{blue}{+10} \\\Leftrightarrow &x & = &15\\\Leftrightarrow & \color{red}{}x & = &15\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 15 \\\Leftrightarrow & \color{green}{ x = 15 } & & \\ & V = \left\{ 15 \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{-15}& = & -8 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{-15}\color{blue}{+15-9x } & = & -8 \color{red}{ +9x }\color{blue}{+15-9x } \\\Leftrightarrow & -11x \color{blue}{-9x } & = & -8 \color{blue}{+15} \\\Leftrightarrow &-20x & = &7\\\Leftrightarrow & \color{red}{-20}x & = &7\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{7}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{20} } & & \\ & V = \left\{ \frac{-7}{20} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{+3}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+3}\color{blue}{-3-x } & = & -5 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -5 \color{blue}{-3} \\\Leftrightarrow &-10x & = &-8\\\Leftrightarrow & \color{red}{-10}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-8}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{-13}& = & -8 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{-13}\color{blue}{+13+11x } & = & -8 \color{red}{ -11x }\color{blue}{+13+11x } \\\Leftrightarrow & 14x \color{blue}{+11x } & = & -8 \color{blue}{+13} \\\Leftrightarrow &25x & = &5\\\Leftrightarrow & \color{red}{25}x & = &5\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{5}{25} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{+1}& = & -11 \color{red}{ +4x } \\\Leftrightarrow & x \color{red}{+1}\color{blue}{-1-4x } & = & -11 \color{red}{ +4x }\color{blue}{-1-4x } \\\Leftrightarrow & x \color{blue}{-4x } & = & -11 \color{blue}{-1} \\\Leftrightarrow &-3x & = &-12\\\Leftrightarrow & \color{red}{-3}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-12}{-3} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{+5}& = & 4 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{+5}\color{blue}{-5-4x } & = & 4 \color{red}{ +4x }\color{blue}{-5-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & 4 \color{blue}{-5} \\\Leftrightarrow &-19x & = &-1\\\Leftrightarrow & \color{red}{-19}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-1}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{1}{19} } & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{-11}& = & 10 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-11}\color{blue}{+11-13x } & = & 10 \color{red}{ +13x }\color{blue}{+11-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 10 \color{blue}{+11} \\\Leftrightarrow &-28x & = &21\\\Leftrightarrow & \color{red}{-28}x & = &21\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{21}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{-13}& = & -14 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{-13}\color{blue}{+13+7x } & = & -14 \color{red}{ -7x }\color{blue}{+13+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & -14 \color{blue}{+13} \\\Leftrightarrow &19x & = &-1\\\Leftrightarrow & \color{red}{19}x & = &-1\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-1}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{19} } & & \\ & V = \left\{ \frac{-1}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{-7}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-7}\color{blue}{+7-x } & = & 8 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 8 \color{blue}{+7} \\\Leftrightarrow &-16x & = &15\\\Leftrightarrow & \color{red}{-16}x & = &15\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{15}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{16} } & & \\ & V = \left\{ \frac{-15}{16} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{+4}& = & -11 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+4}\color{blue}{-4+7x } & = & -11 \color{red}{ -7x }\color{blue}{-4+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -11 \color{blue}{-4} \\\Leftrightarrow &15x & = &-15\\\Leftrightarrow & \color{red}{15}x & = &-15\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-15}{15} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{+2}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+2}\color{blue}{-2-x } & = & 12 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 12 \color{blue}{-2} \\\Leftrightarrow &-14x & = &10\\\Leftrightarrow & \color{red}{-14}x & = &10\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{10}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{-11}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & 8x \color{red}{-11}\color{blue}{+11-7x } & = & -3 \color{red}{ +7x }\color{blue}{+11-7x } \\\Leftrightarrow & 8x \color{blue}{-7x } & = & -3 \color{blue}{+11} \\\Leftrightarrow &x & = &8\\\Leftrightarrow & \color{red}{}x & = &8\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 8 \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)