Vgln. eerste graad (reeks 4)

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1. \(\frac{x}{5}+\frac{5}{12}=\frac{5}{4}x+2\)
2. \(\frac{x}{3}-\frac{3}{17}=\frac{5}{4}x+3\)
3. \(\frac{x}{7}-\frac{4}{17}=\frac{1}{3}x+8\)
4. \(\frac{x}{7}+\frac{4}{11}=\frac{1}{4}x-1\)
5. \(\frac{x}{5}+\frac{4}{17}=\frac{1}{2}x+3\)
6. \(\frac{x}{5}-\frac{4}{7}=\frac{-3}{7}x-7\)
7. \(\frac{x}{6}+\frac{3}{11}=\frac{1}{5}x-1\)
8. \(\frac{x}{4}-\frac{2}{11}=\frac{1}{7}x+5\)
9. \(\frac{x}{3}+\frac{3}{10}=\frac{-2}{7}x-4\)
10. \(\frac{x}{4}+\frac{4}{11}=\frac{-2}{3}x-8\)
11. \(\frac{x}{4}+\frac{2}{7}=\frac{-2}{3}x-5\)
12. \(\frac{x}{4}+\frac{4}{7}=\frac{1}{7}x-7\)

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Reeks met breuken waarbij we ervoor kiezen om de breuken weg te werken. Neem je ZRM!

Verbetersleutel

1. \(\text{60 is het kleinste gemene veelvoud van 5, 12 en 4} \\ \begin{align} & \color{blue}{60.} (\frac{x}{5}+\frac{5}{12})& = & (\frac{5}{4}x+2) \color{blue}{.60} \\\Leftrightarrow & 12x+25& = & 75x+120 \\\Leftrightarrow & 12x \color{red}{+25} \color{blue}{-25} \color{blue}{-75x} & = & \color{red}{75x} +120 \color{blue}{-75x} \color{blue}{-25} \\\Leftrightarrow & -63x& = & 95 \\\Leftrightarrow & \frac{-63x}{ \color{red}{-63} }& = & \frac{95}{-63} \\\Leftrightarrow & x = \frac{-95}{63} & & \\ & V = \left\{ \frac{-95}{63} \right\} & \\\end{align}\)
2. \(\text{204 is het kleinste gemene veelvoud van 3, 17 en 4} \\ \begin{align} & \color{blue}{204.} (\frac{x}{3}-\frac{3}{17})& = & (\frac{5}{4}x+3) \color{blue}{.204} \\\Leftrightarrow & 68x-36& = & 255x+612 \\\Leftrightarrow & 68x \color{red}{-36} \color{blue}{+36} \color{blue}{-255x} & = & \color{red}{255x} +612 \color{blue}{-255x} \color{blue}{+36} \\\Leftrightarrow & -187x& = & 648 \\\Leftrightarrow & \frac{-187x}{ \color{red}{-187} }& = & \frac{648}{-187} \\\Leftrightarrow & x = \frac{-648}{187} & & \\ & V = \left\{ \frac{-648}{187} \right\} & \\\end{align}\)
3. \(\text{357 is het kleinste gemene veelvoud van 7, 17 en 3} \\ \begin{align} & \color{blue}{357.} (\frac{x}{7}-\frac{4}{17})& = & (\frac{1}{3}x+8) \color{blue}{.357} \\\Leftrightarrow & 51x-84& = & 119x+2856 \\\Leftrightarrow & 51x \color{red}{-84} \color{blue}{+84} \color{blue}{-119x} & = & \color{red}{119x} +2856 \color{blue}{-119x} \color{blue}{+84} \\\Leftrightarrow & -68x& = & 2940 \\\Leftrightarrow & \frac{-68x}{ \color{red}{-68} }& = & \frac{2940}{-68} \\\Leftrightarrow & x = \frac{-735}{17} & & \\ & V = \left\{ \frac{-735}{17} \right\} & \\\end{align}\)
4. \(\text{308 is het kleinste gemene veelvoud van 7, 11 en 4} \\ \begin{align} & \color{blue}{308.} (\frac{x}{7}+\frac{4}{11})& = & (\frac{1}{4}x-1) \color{blue}{.308} \\\Leftrightarrow & 44x+112& = & 77x-308 \\\Leftrightarrow & 44x \color{red}{+112} \color{blue}{-112} \color{blue}{-77x} & = & \color{red}{77x} -308 \color{blue}{-77x} \color{blue}{-112} \\\Leftrightarrow & -33x& = & -420 \\\Leftrightarrow & \frac{-33x}{ \color{red}{-33} }& = & \frac{-420}{-33} \\\Leftrightarrow & x = \frac{140}{11} & & \\ & V = \left\{ \frac{140}{11} \right\} & \\\end{align}\)
5. \(\text{170 is het kleinste gemene veelvoud van 5, 17 en 2} \\ \begin{align} & \color{blue}{170.} (\frac{x}{5}+\frac{4}{17})& = & (\frac{1}{2}x+3) \color{blue}{.170} \\\Leftrightarrow & 34x+40& = & 85x+510 \\\Leftrightarrow & 34x \color{red}{+40} \color{blue}{-40} \color{blue}{-85x} & = & \color{red}{85x} +510 \color{blue}{-85x} \color{blue}{-40} \\\Leftrightarrow & -51x& = & 470 \\\Leftrightarrow & \frac{-51x}{ \color{red}{-51} }& = & \frac{470}{-51} \\\Leftrightarrow & x = \frac{-470}{51} & & \\ & V = \left\{ \frac{-470}{51} \right\} & \\\end{align}\)
6. \(\text{35 is het kleinste gemene veelvoud van 5, 7 en 7} \\ \begin{align} & \color{blue}{35.} (\frac{x}{5}-\frac{4}{7})& = & (\frac{-3}{7}x-7) \color{blue}{.35} \\\Leftrightarrow & 7x-20& = & -15x-245 \\\Leftrightarrow & 7x \color{red}{-20} \color{blue}{+20} \color{blue}{+15x} & = & \color{red}{-15x} -245 \color{blue}{+15x} \color{blue}{+20} \\\Leftrightarrow & 22x& = & -225 \\\Leftrightarrow & \frac{22x}{ \color{red}{22} }& = & \frac{-225}{22} \\\Leftrightarrow & x = \frac{-225}{22} & & \\ & V = \left\{ \frac{-225}{22} \right\} & \\\end{align}\)
7. \(\text{330 is het kleinste gemene veelvoud van 6, 11 en 5} \\ \begin{align} & \color{blue}{330.} (\frac{x}{6}+\frac{3}{11})& = & (\frac{1}{5}x-1) \color{blue}{.330} \\\Leftrightarrow & 55x+90& = & 66x-330 \\\Leftrightarrow & 55x \color{red}{+90} \color{blue}{-90} \color{blue}{-66x} & = & \color{red}{66x} -330 \color{blue}{-66x} \color{blue}{-90} \\\Leftrightarrow & -11x& = & -420 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = & \frac{-420}{-11} \\\Leftrightarrow & x = \frac{420}{11} & & \\ & V = \left\{ \frac{420}{11} \right\} & \\\end{align}\)
8. \(\text{308 is het kleinste gemene veelvoud van 4, 11 en 7} \\ \begin{align} & \color{blue}{308.} (\frac{x}{4}-\frac{2}{11})& = & (\frac{1}{7}x+5) \color{blue}{.308} \\\Leftrightarrow & 77x-56& = & 44x+1540 \\\Leftrightarrow & 77x \color{red}{-56} \color{blue}{+56} \color{blue}{-44x} & = & \color{red}{44x} +1540 \color{blue}{-44x} \color{blue}{+56} \\\Leftrightarrow & 33x& = & 1596 \\\Leftrightarrow & \frac{33x}{ \color{red}{33} }& = & \frac{1596}{33} \\\Leftrightarrow & x = \frac{532}{11} & & \\ & V = \left\{ \frac{532}{11} \right\} & \\\end{align}\)
9. \(\text{210 is het kleinste gemene veelvoud van 3, 10 en 7} \\ \begin{align} & \color{blue}{210.} (\frac{x}{3}+\frac{3}{10})& = & (\frac{-2}{7}x-4) \color{blue}{.210} \\\Leftrightarrow & 70x+63& = & -60x-840 \\\Leftrightarrow & 70x \color{red}{+63} \color{blue}{-63} \color{blue}{+60x} & = & \color{red}{-60x} -840 \color{blue}{+60x} \color{blue}{-63} \\\Leftrightarrow & 130x& = & -903 \\\Leftrightarrow & \frac{130x}{ \color{red}{130} }& = & \frac{-903}{130} \\\Leftrightarrow & x = \frac{-903}{130} & & \\ & V = \left\{ \frac{-903}{130} \right\} & \\\end{align}\)
10. \(\text{132 is het kleinste gemene veelvoud van 4, 11 en 3} \\ \begin{align} & \color{blue}{132.} (\frac{x}{4}+\frac{4}{11})& = & (\frac{-2}{3}x-8) \color{blue}{.132} \\\Leftrightarrow & 33x+48& = & -88x-1056 \\\Leftrightarrow & 33x \color{red}{+48} \color{blue}{-48} \color{blue}{+88x} & = & \color{red}{-88x} -1056 \color{blue}{+88x} \color{blue}{-48} \\\Leftrightarrow & 121x& = & -1104 \\\Leftrightarrow & \frac{121x}{ \color{red}{121} }& = & \frac{-1104}{121} \\\Leftrightarrow & x = \frac{-1104}{121} & & \\ & V = \left\{ \frac{-1104}{121} \right\} & \\\end{align}\)
11. \(\text{84 is het kleinste gemene veelvoud van 4, 7 en 3} \\ \begin{align} & \color{blue}{84.} (\frac{x}{4}+\frac{2}{7})& = & (\frac{-2}{3}x-5) \color{blue}{.84} \\\Leftrightarrow & 21x+24& = & -56x-420 \\\Leftrightarrow & 21x \color{red}{+24} \color{blue}{-24} \color{blue}{+56x} & = & \color{red}{-56x} -420 \color{blue}{+56x} \color{blue}{-24} \\\Leftrightarrow & 77x& = & -444 \\\Leftrightarrow & \frac{77x}{ \color{red}{77} }& = & \frac{-444}{77} \\\Leftrightarrow & x = \frac{-444}{77} & & \\ & V = \left\{ \frac{-444}{77} \right\} & \\\end{align}\)
12. \(\text{28 is het kleinste gemene veelvoud van 4, 7 en 7} \\ \begin{align} & \color{blue}{28.} (\frac{x}{4}+\frac{4}{7})& = & (\frac{1}{7}x-7) \color{blue}{.28} \\\Leftrightarrow & 7x+16& = & 4x-196 \\\Leftrightarrow & 7x \color{red}{+16} \color{blue}{-16} \color{blue}{-4x} & = & \color{red}{4x} -196 \color{blue}{-4x} \color{blue}{-16} \\\Leftrightarrow & 3x& = & -212 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = & \frac{-212}{3} \\\Leftrightarrow & x = \frac{-212}{3} & & \\ & V = \left\{ \frac{-212}{3} \right\} & \\\end{align}\)