Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{3}{11})& = & 3x+\frac{8}{11} \\\Leftrightarrow & 8x+\frac{12}{11}& = & 3x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{88}{ \color{blue}{11} }x+ \frac{12}{ \color{blue}{11} })& = & (\frac{33}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 88x \color{red}{+12} & = & \color{red}{33x} +8 \\\Leftrightarrow & 88x \color{red}{+12} \color{blue}{-12} \color{blue}{-33x} & = & \color{red}{33x} +8 \color{blue}{-33x} \color{blue}{-12} \\\Leftrightarrow & 88x-33x& = & 8-12 \\\Leftrightarrow & \color{red}{55} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{55} & & \\ & V = \left\{ \frac{-4}{55} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{5}{7})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -18x-\frac{30}{7}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-378}{ \color{blue}{21} }x- \frac{90}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -378x \color{red}{-90} & = & \color{red}{-147x} +28 \\\Leftrightarrow & -378x \color{red}{-90} \color{blue}{+90} \color{blue}{+147x} & = & \color{red}{-147x} +28 \color{blue}{+147x} \color{blue}{+90} \\\Leftrightarrow & -378x+147x& = & 28+90 \\\Leftrightarrow & \color{red}{-231} x& = & 118 \\\Leftrightarrow & x = \frac{118}{-231} & & \\\Leftrightarrow & x = \frac{-118}{231} & & \\ & V = \left\{ \frac{-118}{231} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{3}{7})& = & -7x+\frac{9}{4} \\\Leftrightarrow & 6x+\frac{6}{7}& = & -7x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{168}{ \color{blue}{28} }x+ \frac{24}{ \color{blue}{28} })& = & (\frac{-196}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 168x \color{red}{+24} & = & \color{red}{-196x} +63 \\\Leftrightarrow & 168x \color{red}{+24} \color{blue}{-24} \color{blue}{+196x} & = & \color{red}{-196x} +63 \color{blue}{+196x} \color{blue}{-24} \\\Leftrightarrow & 168x+196x& = & 63-24 \\\Leftrightarrow & \color{red}{364} x& = & 39 \\\Leftrightarrow & x = \frac{39}{364} & & \\\Leftrightarrow & x = \frac{3}{28} & & \\ & V = \left\{ \frac{3}{28} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{2}{7})& = & -5x+\frac{7}{12} \\\Leftrightarrow & 6x-\frac{6}{7}& = & -5x+\frac{7}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{504}{ \color{blue}{84} }x- \frac{72}{ \color{blue}{84} })& = & (\frac{-420}{ \color{blue}{84} }x+ \frac{49}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & 504x \color{red}{-72} & = & \color{red}{-420x} +49 \\\Leftrightarrow & 504x \color{red}{-72} \color{blue}{+72} \color{blue}{+420x} & = & \color{red}{-420x} +49 \color{blue}{+420x} \color{blue}{+72} \\\Leftrightarrow & 504x+420x& = & 49+72 \\\Leftrightarrow & \color{red}{924} x& = & 121 \\\Leftrightarrow & x = \frac{121}{924} & & \\\Leftrightarrow & x = \frac{11}{84} & & \\ & V = \left\{ \frac{11}{84} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{2}{7})& = & -7x+\frac{5}{11} \\\Leftrightarrow & 6x+\frac{6}{7}& = & -7x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{462}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 462x \color{red}{+66} & = & \color{red}{-539x} +35 \\\Leftrightarrow & 462x \color{red}{+66} \color{blue}{-66} \color{blue}{+539x} & = & \color{red}{-539x} +35 \color{blue}{+539x} \color{blue}{-66} \\\Leftrightarrow & 462x+539x& = & 35-66 \\\Leftrightarrow & \color{red}{1001} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{1001} & & \\ & V = \left\{ \frac{-31}{1001} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{5}{11})& = & -5x+\frac{7}{8} \\\Leftrightarrow & -24x+\frac{30}{11}& = & -5x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-2112}{ \color{blue}{88} }x+ \frac{240}{ \color{blue}{88} })& = & (\frac{-440}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -2112x \color{red}{+240} & = & \color{red}{-440x} +77 \\\Leftrightarrow & -2112x \color{red}{+240} \color{blue}{-240} \color{blue}{+440x} & = & \color{red}{-440x} +77 \color{blue}{+440x} \color{blue}{-240} \\\Leftrightarrow & -2112x+440x& = & 77-240 \\\Leftrightarrow & \color{red}{-1672} x& = & -163 \\\Leftrightarrow & x = \frac{-163}{-1672} & & \\\Leftrightarrow & x = \frac{163}{1672} & & \\ & V = \left\{ \frac{163}{1672} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{5}{7})& = & -3x+\frac{6}{11} \\\Leftrightarrow & 8x-\frac{20}{7}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{616}{ \color{blue}{77} }x- \frac{220}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 616x \color{red}{-220} & = & \color{red}{-231x} +42 \\\Leftrightarrow & 616x \color{red}{-220} \color{blue}{+220} \color{blue}{+231x} & = & \color{red}{-231x} +42 \color{blue}{+231x} \color{blue}{+220} \\\Leftrightarrow & 616x+231x& = & 42+220 \\\Leftrightarrow & \color{red}{847} x& = & 262 \\\Leftrightarrow & x = \frac{262}{847} & & \\ & V = \left\{ \frac{262}{847} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{3}{2})& = & -2x+\frac{10}{11} \\\Leftrightarrow & 21x-\frac{21}{2}& = & -2x+\frac{10}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{462}{ \color{blue}{22} }x- \frac{231}{ \color{blue}{22} })& = & (\frac{-44}{ \color{blue}{22} }x+ \frac{20}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 462x \color{red}{-231} & = & \color{red}{-44x} +20 \\\Leftrightarrow & 462x \color{red}{-231} \color{blue}{+231} \color{blue}{+44x} & = & \color{red}{-44x} +20 \color{blue}{+44x} \color{blue}{+231} \\\Leftrightarrow & 462x+44x& = & 20+231 \\\Leftrightarrow & \color{red}{506} x& = & 251 \\\Leftrightarrow & x = \frac{251}{506} & & \\ & V = \left\{ \frac{251}{506} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{4}{9})& = & 6x+\frac{4}{5} \\\Leftrightarrow & 35x+\frac{28}{9}& = & 6x+\frac{4}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{1575}{ \color{blue}{45} }x+ \frac{140}{ \color{blue}{45} })& = & (\frac{270}{ \color{blue}{45} }x+ \frac{36}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 1575x \color{red}{+140} & = & \color{red}{270x} +36 \\\Leftrightarrow & 1575x \color{red}{+140} \color{blue}{-140} \color{blue}{-270x} & = & \color{red}{270x} +36 \color{blue}{-270x} \color{blue}{-140} \\\Leftrightarrow & 1575x-270x& = & 36-140 \\\Leftrightarrow & \color{red}{1305} x& = & -104 \\\Leftrightarrow & x = \frac{-104}{1305} & & \\ & V = \left\{ \frac{-104}{1305} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{2}{9})& = & 3x+\frac{6}{7} \\\Leftrightarrow & -20x+\frac{8}{9}& = & 3x+\frac{6}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1260}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} })& = & (\frac{189}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1260x \color{red}{+56} & = & \color{red}{189x} +54 \\\Leftrightarrow & -1260x \color{red}{+56} \color{blue}{-56} \color{blue}{-189x} & = & \color{red}{189x} +54 \color{blue}{-189x} \color{blue}{-56} \\\Leftrightarrow & -1260x-189x& = & 54-56 \\\Leftrightarrow & \color{red}{-1449} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-1449} & & \\\Leftrightarrow & x = \frac{2}{1449} & & \\ & V = \left\{ \frac{2}{1449} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{5}{4})& = & 2x+\frac{4}{11} \\\Leftrightarrow & 9x-\frac{15}{4}& = & 2x+\frac{4}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{396}{ \color{blue}{44} }x- \frac{165}{ \color{blue}{44} })& = & (\frac{88}{ \color{blue}{44} }x+ \frac{16}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 396x \color{red}{-165} & = & \color{red}{88x} +16 \\\Leftrightarrow & 396x \color{red}{-165} \color{blue}{+165} \color{blue}{-88x} & = & \color{red}{88x} +16 \color{blue}{-88x} \color{blue}{+165} \\\Leftrightarrow & 396x-88x& = & 16+165 \\\Leftrightarrow & \color{red}{308} x& = & 181 \\\Leftrightarrow & x = \frac{181}{308} & & \\ & V = \left\{ \frac{181}{308} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{3}{5})& = & -5x+\frac{3}{2} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{+24} & = & \color{red}{-50x} +15 \\\Leftrightarrow & 120x \color{red}{+24} \color{blue}{-24} \color{blue}{+50x} & = & \color{red}{-50x} +15 \color{blue}{+50x} \color{blue}{-24} \\\Leftrightarrow & 120x+50x& = & 15-24 \\\Leftrightarrow & \color{red}{170} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{170} & & \\ & V = \left\{ \frac{-9}{170} \right\} & \\\end{align}\)