Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{-4}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-4}\color{blue}{+4-x } & = & -10 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -10 \color{blue}{+4} \\\Leftrightarrow &-9x & = &-6\\\Leftrightarrow & \color{red}{-9}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-6}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{-14}& = & 4 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-14}\color{blue}{+14+7x } & = & 4 \color{red}{ -7x }\color{blue}{+14+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 4 \color{blue}{+14} \\\Leftrightarrow &15x & = &18\\\Leftrightarrow & \color{red}{15}x & = &18\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{18}{15} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{+2}& = & -6 \color{red}{ +5x } \\\Leftrightarrow & 14x \color{red}{+2}\color{blue}{-2-5x } & = & -6 \color{red}{ +5x }\color{blue}{-2-5x } \\\Leftrightarrow & 14x \color{blue}{-5x } & = & -6 \color{blue}{-2} \\\Leftrightarrow &9x & = &-8\\\Leftrightarrow & \color{red}{9}x & = &-8\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-8}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{9} } & & \\ & V = \left\{ \frac{-8}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{+14}& = & 10 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+14}\color{blue}{-14-13x } & = & 10 \color{red}{ +13x }\color{blue}{-14-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 10 \color{blue}{-14} \\\Leftrightarrow &-28x & = &-4\\\Leftrightarrow & \color{red}{-28}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-4}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{+15}& = & 2 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{+15}\color{blue}{-15-9x } & = & 2 \color{red}{ +9x }\color{blue}{-15-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & 2 \color{blue}{-15} \\\Leftrightarrow &5x & = &-13\\\Leftrightarrow & \color{red}{5}x & = &-13\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-13}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{5} } & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{+6}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+6}\color{blue}{-6-x } & = & 6 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 6 \color{blue}{-6} \\\Leftrightarrow &-13x & = &0\\\Leftrightarrow & \color{red}{-13}x & = &0\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{0}{-13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{-10}& = & 13 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-10}\color{blue}{+10-13x } & = & 13 \color{red}{ +13x }\color{blue}{+10-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 13 \color{blue}{+10} \\\Leftrightarrow &-28x & = &23\\\Leftrightarrow & \color{red}{-28}x & = &23\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{23}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{28} } & & \\ & V = \left\{ \frac{-23}{28} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{-10}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-10}\color{blue}{+10-x } & = & -1 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -1 \color{blue}{+10} \\\Leftrightarrow &x & = &9\\\Leftrightarrow & \color{red}{}x & = &9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 9 \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{+12}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+12}\color{blue}{-12-x } & = & -6 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -6 \color{blue}{-12} \\\Leftrightarrow &-5x & = &-18\\\Leftrightarrow & \color{red}{-5}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-18}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{18}{5} } & & \\ & V = \left\{ \frac{18}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{+5}& = & -11 \color{red}{ +12x } \\\Leftrightarrow & 7x \color{red}{+5}\color{blue}{-5-12x } & = & -11 \color{red}{ +12x }\color{blue}{-5-12x } \\\Leftrightarrow & 7x \color{blue}{-12x } & = & -11 \color{blue}{-5} \\\Leftrightarrow &-5x & = &-16\\\Leftrightarrow & \color{red}{-5}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-16}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{16}{5} } & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{+4}& = & 3 \color{red}{ -9x } \\\Leftrightarrow & -x \color{red}{+4}\color{blue}{-4+9x } & = & 3 \color{red}{ -9x }\color{blue}{-4+9x } \\\Leftrightarrow & -x \color{blue}{+9x } & = & 3 \color{blue}{-4} \\\Leftrightarrow &8x & = &-1\\\Leftrightarrow & \color{red}{8}x & = &-1\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-1}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{+2}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+2}\color{blue}{-2-x } & = & -10 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -10 \color{blue}{-2} \\\Leftrightarrow &-5x & = &-12\\\Leftrightarrow & \color{red}{-5}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-12}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)