Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{4}{3})& = & 7x+\frac{3}{5} \\\Leftrightarrow & -6x-\frac{8}{3}& = & 7x+\frac{3}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-90}{ \color{blue}{15} }x- \frac{40}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{9}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -90x \color{red}{-40} & = & \color{red}{105x} +9 \\\Leftrightarrow & -90x \color{red}{-40} \color{blue}{+40} \color{blue}{-105x} & = & \color{red}{105x} +9 \color{blue}{-105x} \color{blue}{+40} \\\Leftrightarrow & -90x-105x& = & 9+40 \\\Leftrightarrow & \color{red}{-195} x& = & 49 \\\Leftrightarrow & x = \frac{49}{-195} & & \\\Leftrightarrow & x = \frac{-49}{195} & & \\ & V = \left\{ \frac{-49}{195} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{3}{11})& = & -9x+\frac{3}{8} \\\Leftrightarrow & -28x+\frac{21}{11}& = & -9x+\frac{3}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-2464}{ \color{blue}{88} }x+ \frac{168}{ \color{blue}{88} })& = & (\frac{-792}{ \color{blue}{88} }x+ \frac{33}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -2464x \color{red}{+168} & = & \color{red}{-792x} +33 \\\Leftrightarrow & -2464x \color{red}{+168} \color{blue}{-168} \color{blue}{+792x} & = & \color{red}{-792x} +33 \color{blue}{+792x} \color{blue}{-168} \\\Leftrightarrow & -2464x+792x& = & 33-168 \\\Leftrightarrow & \color{red}{-1672} x& = & -135 \\\Leftrightarrow & x = \frac{-135}{-1672} & & \\\Leftrightarrow & x = \frac{135}{1672} & & \\ & V = \left\{ \frac{135}{1672} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{5}{9})& = & 8x+\frac{6}{5} \\\Leftrightarrow & 21x-\frac{35}{9}& = & 8x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{945}{ \color{blue}{45} }x- \frac{175}{ \color{blue}{45} })& = & (\frac{360}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 945x \color{red}{-175} & = & \color{red}{360x} +54 \\\Leftrightarrow & 945x \color{red}{-175} \color{blue}{+175} \color{blue}{-360x} & = & \color{red}{360x} +54 \color{blue}{-360x} \color{blue}{+175} \\\Leftrightarrow & 945x-360x& = & 54+175 \\\Leftrightarrow & \color{red}{585} x& = & 229 \\\Leftrightarrow & x = \frac{229}{585} & & \\ & V = \left\{ \frac{229}{585} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{5}{4})& = & -5x+\frac{4}{11} \\\Leftrightarrow & 6x+\frac{15}{4}& = & -5x+\frac{4}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{264}{ \color{blue}{44} }x+ \frac{165}{ \color{blue}{44} })& = & (\frac{-220}{ \color{blue}{44} }x+ \frac{16}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 264x \color{red}{+165} & = & \color{red}{-220x} +16 \\\Leftrightarrow & 264x \color{red}{+165} \color{blue}{-165} \color{blue}{+220x} & = & \color{red}{-220x} +16 \color{blue}{+220x} \color{blue}{-165} \\\Leftrightarrow & 264x+220x& = & 16-165 \\\Leftrightarrow & \color{red}{484} x& = & -149 \\\Leftrightarrow & x = \frac{-149}{484} & & \\ & V = \left\{ \frac{-149}{484} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{4}{5})& = & 5x+\frac{3}{8} \\\Leftrightarrow & -12x-\frac{16}{5}& = & 5x+\frac{3}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-480}{ \color{blue}{40} }x- \frac{128}{ \color{blue}{40} })& = & (\frac{200}{ \color{blue}{40} }x+ \frac{15}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -480x \color{red}{-128} & = & \color{red}{200x} +15 \\\Leftrightarrow & -480x \color{red}{-128} \color{blue}{+128} \color{blue}{-200x} & = & \color{red}{200x} +15 \color{blue}{-200x} \color{blue}{+128} \\\Leftrightarrow & -480x-200x& = & 15+128 \\\Leftrightarrow & \color{red}{-680} x& = & 143 \\\Leftrightarrow & x = \frac{143}{-680} & & \\\Leftrightarrow & x = \frac{-143}{680} & & \\ & V = \left\{ \frac{-143}{680} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{3}{11})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -30x-\frac{18}{11}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-330}{ \color{blue}{11} }x- \frac{18}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -330x \color{red}{-18} & = & \color{red}{77x} +6 \\\Leftrightarrow & -330x \color{red}{-18} \color{blue}{+18} \color{blue}{-77x} & = & \color{red}{77x} +6 \color{blue}{-77x} \color{blue}{+18} \\\Leftrightarrow & -330x-77x& = & 6+18 \\\Leftrightarrow & \color{red}{-407} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-407} & & \\\Leftrightarrow & x = \frac{-24}{407} & & \\ & V = \left\{ \frac{-24}{407} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{2}{11})& = & 4x+\frac{9}{4} \\\Leftrightarrow & -15x+\frac{10}{11}& = & 4x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-660}{ \color{blue}{44} }x+ \frac{40}{ \color{blue}{44} })& = & (\frac{176}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -660x \color{red}{+40} & = & \color{red}{176x} +99 \\\Leftrightarrow & -660x \color{red}{+40} \color{blue}{-40} \color{blue}{-176x} & = & \color{red}{176x} +99 \color{blue}{-176x} \color{blue}{-40} \\\Leftrightarrow & -660x-176x& = & 99-40 \\\Leftrightarrow & \color{red}{-836} x& = & 59 \\\Leftrightarrow & x = \frac{59}{-836} & & \\\Leftrightarrow & x = \frac{-59}{836} & & \\ & V = \left\{ \frac{-59}{836} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{2}{11})& = & -5x+\frac{10}{9} \\\Leftrightarrow & 12x+\frac{8}{11}& = & -5x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1188}{ \color{blue}{99} }x+ \frac{72}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1188x \color{red}{+72} & = & \color{red}{-495x} +110 \\\Leftrightarrow & 1188x \color{red}{+72} \color{blue}{-72} \color{blue}{+495x} & = & \color{red}{-495x} +110 \color{blue}{+495x} \color{blue}{-72} \\\Leftrightarrow & 1188x+495x& = & 110-72 \\\Leftrightarrow & \color{red}{1683} x& = & 38 \\\Leftrightarrow & x = \frac{38}{1683} & & \\ & V = \left\{ \frac{38}{1683} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{4}{7})& = & -7x+\frac{10}{9} \\\Leftrightarrow & 15x+\frac{12}{7}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{945}{ \color{blue}{63} }x+ \frac{108}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 945x \color{red}{+108} & = & \color{red}{-441x} +70 \\\Leftrightarrow & 945x \color{red}{+108} \color{blue}{-108} \color{blue}{+441x} & = & \color{red}{-441x} +70 \color{blue}{+441x} \color{blue}{-108} \\\Leftrightarrow & 945x+441x& = & 70-108 \\\Leftrightarrow & \color{red}{1386} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{1386} & & \\\Leftrightarrow & x = \frac{-19}{693} & & \\ & V = \left\{ \frac{-19}{693} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{3}{4})& = & -5x+\frac{3}{2} \\\Leftrightarrow & -9x-\frac{9}{4}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-36}{ \color{blue}{4} }x- \frac{9}{ \color{blue}{4} })& = & (\frac{-20}{ \color{blue}{4} }x+ \frac{6}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -36x \color{red}{-9} & = & \color{red}{-20x} +6 \\\Leftrightarrow & -36x \color{red}{-9} \color{blue}{+9} \color{blue}{+20x} & = & \color{red}{-20x} +6 \color{blue}{+20x} \color{blue}{+9} \\\Leftrightarrow & -36x+20x& = & 6+9 \\\Leftrightarrow & \color{red}{-16} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-16} & & \\\Leftrightarrow & x = \frac{-15}{16} & & \\ & V = \left\{ \frac{-15}{16} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{5}{8})& = & -7x+\frac{9}{7} \\\Leftrightarrow & 10x-\frac{25}{8}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{560}{ \color{blue}{56} }x- \frac{175}{ \color{blue}{56} })& = & (\frac{-392}{ \color{blue}{56} }x+ \frac{72}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 560x \color{red}{-175} & = & \color{red}{-392x} +72 \\\Leftrightarrow & 560x \color{red}{-175} \color{blue}{+175} \color{blue}{+392x} & = & \color{red}{-392x} +72 \color{blue}{+392x} \color{blue}{+175} \\\Leftrightarrow & 560x+392x& = & 72+175 \\\Leftrightarrow & \color{red}{952} x& = & 247 \\\Leftrightarrow & x = \frac{247}{952} & & \\ & V = \left\{ \frac{247}{952} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{2}{5})& = & -7x+\frac{3}{2} \\\Leftrightarrow & -24x+\frac{12}{5}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-240}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -240x \color{red}{+24} & = & \color{red}{-70x} +15 \\\Leftrightarrow & -240x \color{red}{+24} \color{blue}{-24} \color{blue}{+70x} & = & \color{red}{-70x} +15 \color{blue}{+70x} \color{blue}{-24} \\\Leftrightarrow & -240x+70x& = & 15-24 \\\Leftrightarrow & \color{red}{-170} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-170} & & \\\Leftrightarrow & x = \frac{9}{170} & & \\ & V = \left\{ \frac{9}{170} \right\} & \\\end{align}\)