Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{+3}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+3}\color{blue}{-3-x } & = & 7 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 7 \color{blue}{-3} \\\Leftrightarrow &-6x & = &4\\\Leftrightarrow & \color{red}{-6}x & = &4\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{4}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{-10}& = & 13 \color{red}{ +6x } \\\Leftrightarrow & 7x \color{red}{-10}\color{blue}{+10-6x } & = & 13 \color{red}{ +6x }\color{blue}{+10-6x } \\\Leftrightarrow & 7x \color{blue}{-6x } & = & 13 \color{blue}{+10} \\\Leftrightarrow &x & = &23\\\Leftrightarrow & \color{red}{}x & = &23\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 23 \\\Leftrightarrow & \color{green}{ x = 23 } & & \\ & V = \left\{ 23 \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{-5}& = & 5 \color{red}{ -8x } \\\Leftrightarrow & 11x \color{red}{-5}\color{blue}{+5+8x } & = & 5 \color{red}{ -8x }\color{blue}{+5+8x } \\\Leftrightarrow & 11x \color{blue}{+8x } & = & 5 \color{blue}{+5} \\\Leftrightarrow &19x & = &10\\\Leftrightarrow & \color{red}{19}x & = &10\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{10}{19} \\\Leftrightarrow & \color{green}{ x = \frac{10}{19} } & & \\ & V = \left\{ \frac{10}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{+9}& = & -1 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{+9}\color{blue}{-9-14x } & = & -1 \color{red}{ +14x }\color{blue}{-9-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & -1 \color{blue}{-9} \\\Leftrightarrow &-25x & = &-10\\\Leftrightarrow & \color{red}{-25}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-10}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{+5}& = & 15 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+5}\color{blue}{-5+5x } & = & 15 \color{red}{ -5x }\color{blue}{-5+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 15 \color{blue}{-5} \\\Leftrightarrow &11x & = &10\\\Leftrightarrow & \color{red}{11}x & = &10\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{10}{11} \\\Leftrightarrow & \color{green}{ x = \frac{10}{11} } & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{-3}& = & 13 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{-3}\color{blue}{+3-6x } & = & 13 \color{red}{ +6x }\color{blue}{+3-6x } \\\Leftrightarrow & -11x \color{blue}{-6x } & = & 13 \color{blue}{+3} \\\Leftrightarrow &-17x & = &16\\\Leftrightarrow & \color{red}{-17}x & = &16\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{16}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{17} } & & \\ & V = \left\{ \frac{-16}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{+5}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+5}\color{blue}{-5-13x } & = & 14 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 14 \color{blue}{-5} \\\Leftrightarrow &-28x & = &9\\\Leftrightarrow & \color{red}{-28}x & = &9\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{9}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{28} } & & \\ & V = \left\{ \frac{-9}{28} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{-1}& = & -3 \color{red}{ -x } \\\Leftrightarrow & x \color{red}{-1}\color{blue}{+1+x } & = & -3 \color{red}{ -x }\color{blue}{+1+x } \\\Leftrightarrow & x \color{blue}{+x } & = & -3 \color{blue}{+1} \\\Leftrightarrow &2x & = &-2\\\Leftrightarrow & \color{red}{2}x & = &-2\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-2}{2} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{+2}& = & 14 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{+2}\color{blue}{-2+11x } & = & 14 \color{red}{ -11x }\color{blue}{-2+11x } \\\Leftrightarrow & 9x \color{blue}{+11x } & = & 14 \color{blue}{-2} \\\Leftrightarrow &20x & = &12\\\Leftrightarrow & \color{red}{20}x & = &12\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{12}{20} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{-4}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-4}\color{blue}{+4-x } & = & -12 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -12 \color{blue}{+4} \\\Leftrightarrow &-14x & = &-8\\\Leftrightarrow & \color{red}{-14}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-8}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{-12}& = & 3 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{-12}\color{blue}{+12+15x } & = & 3 \color{red}{ -15x }\color{blue}{+12+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & 3 \color{blue}{+12} \\\Leftrightarrow &19x & = &15\\\Leftrightarrow & \color{red}{19}x & = &15\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{15}{19} \\\Leftrightarrow & \color{green}{ x = \frac{15}{19} } & & \\ & V = \left\{ \frac{15}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{+7}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+7}\color{blue}{-7-x } & = & 13 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 13 \color{blue}{-7} \\\Leftrightarrow &-14x & = &6\\\Leftrightarrow & \color{red}{-14}x & = &6\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{6}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)