Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{2}{3})& = & -6x+\frac{9}{11} \\\Leftrightarrow & -25x-\frac{10}{3}& = & -6x+\frac{9}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-825}{ \color{blue}{33} }x- \frac{110}{ \color{blue}{33} })& = & (\frac{-198}{ \color{blue}{33} }x+ \frac{27}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -825x \color{red}{-110} & = & \color{red}{-198x} +27 \\\Leftrightarrow & -825x \color{red}{-110} \color{blue}{+110} \color{blue}{+198x} & = & \color{red}{-198x} +27 \color{blue}{+198x} \color{blue}{+110} \\\Leftrightarrow & -825x+198x& = & 27+110 \\\Leftrightarrow & \color{red}{-627} x& = & 137 \\\Leftrightarrow & x = \frac{137}{-627} & & \\\Leftrightarrow & x = \frac{-137}{627} & & \\ & V = \left\{ \frac{-137}{627} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{3}{11})& = & -5x+\frac{8}{3} \\\Leftrightarrow & 12x+\frac{12}{11}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{396}{ \color{blue}{33} }x+ \frac{36}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 396x \color{red}{+36} & = & \color{red}{-165x} +88 \\\Leftrightarrow & 396x \color{red}{+36} \color{blue}{-36} \color{blue}{+165x} & = & \color{red}{-165x} +88 \color{blue}{+165x} \color{blue}{-36} \\\Leftrightarrow & 396x+165x& = & 88-36 \\\Leftrightarrow & \color{red}{561} x& = & 52 \\\Leftrightarrow & x = \frac{52}{561} & & \\ & V = \left\{ \frac{52}{561} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{2}{3})& = & -9x+\frac{4}{5} \\\Leftrightarrow & -35x+\frac{14}{3}& = & -9x+\frac{4}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-525}{ \color{blue}{15} }x+ \frac{70}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -525x \color{red}{+70} & = & \color{red}{-135x} +12 \\\Leftrightarrow & -525x \color{red}{+70} \color{blue}{-70} \color{blue}{+135x} & = & \color{red}{-135x} +12 \color{blue}{+135x} \color{blue}{-70} \\\Leftrightarrow & -525x+135x& = & 12-70 \\\Leftrightarrow & \color{red}{-390} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{-390} & & \\\Leftrightarrow & x = \frac{29}{195} & & \\ & V = \left\{ \frac{29}{195} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{5}{6})& = & -3x+\frac{4}{9} \\\Leftrightarrow & 10x+\frac{25}{6}& = & -3x+\frac{4}{9} \\ & & & \text{kgv van noemers 6 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{180}{ \color{blue}{18} }x+ \frac{75}{ \color{blue}{18} })& = & (\frac{-54}{ \color{blue}{18} }x+ \frac{8}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 180x \color{red}{+75} & = & \color{red}{-54x} +8 \\\Leftrightarrow & 180x \color{red}{+75} \color{blue}{-75} \color{blue}{+54x} & = & \color{red}{-54x} +8 \color{blue}{+54x} \color{blue}{-75} \\\Leftrightarrow & 180x+54x& = & 8-75 \\\Leftrightarrow & \color{red}{234} x& = & -67 \\\Leftrightarrow & x = \frac{-67}{234} & & \\ & V = \left\{ \frac{-67}{234} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{5}{7})& = & 5x+\frac{7}{2} \\\Leftrightarrow & 18x+\frac{30}{7}& = & 5x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{252}{ \color{blue}{14} }x+ \frac{60}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 252x \color{red}{+60} & = & \color{red}{70x} +49 \\\Leftrightarrow & 252x \color{red}{+60} \color{blue}{-60} \color{blue}{-70x} & = & \color{red}{70x} +49 \color{blue}{-70x} \color{blue}{-60} \\\Leftrightarrow & 252x-70x& = & 49-60 \\\Leftrightarrow & \color{red}{182} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{182} & & \\ & V = \left\{ \frac{-11}{182} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{5}{3})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -10x-\frac{25}{3}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-150}{ \color{blue}{15} }x- \frac{125}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -150x \color{red}{-125} & = & \color{red}{105x} +18 \\\Leftrightarrow & -150x \color{red}{-125} \color{blue}{+125} \color{blue}{-105x} & = & \color{red}{105x} +18 \color{blue}{-105x} \color{blue}{+125} \\\Leftrightarrow & -150x-105x& = & 18+125 \\\Leftrightarrow & \color{red}{-255} x& = & 143 \\\Leftrightarrow & x = \frac{143}{-255} & & \\\Leftrightarrow & x = \frac{-143}{255} & & \\ & V = \left\{ \frac{-143}{255} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{4}{5})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 18x+\frac{24}{5}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{90}{ \color{blue}{5} }x+ \frac{24}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 90x \color{red}{+24} & = & \color{red}{25x} +6 \\\Leftrightarrow & 90x \color{red}{+24} \color{blue}{-24} \color{blue}{-25x} & = & \color{red}{25x} +6 \color{blue}{-25x} \color{blue}{-24} \\\Leftrightarrow & 90x-25x& = & 6-24 \\\Leftrightarrow & \color{red}{65} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{65} & & \\ & V = \left\{ \frac{-18}{65} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{3}{11})& = & -7x+\frac{5}{4} \\\Leftrightarrow & -6x-\frac{6}{11}& = & -7x+\frac{5}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-264}{ \color{blue}{44} }x- \frac{24}{ \color{blue}{44} })& = & (\frac{-308}{ \color{blue}{44} }x+ \frac{55}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -264x \color{red}{-24} & = & \color{red}{-308x} +55 \\\Leftrightarrow & -264x \color{red}{-24} \color{blue}{+24} \color{blue}{+308x} & = & \color{red}{-308x} +55 \color{blue}{+308x} \color{blue}{+24} \\\Leftrightarrow & -264x+308x& = & 55+24 \\\Leftrightarrow & \color{red}{44} x& = & 79 \\\Leftrightarrow & x = \frac{79}{44} & & \\ & V = \left\{ \frac{79}{44} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{4}{5})& = & -5x+\frac{7}{9} \\\Leftrightarrow & -12x+\frac{12}{5}& = & -5x+\frac{7}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-540}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{35}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -540x \color{red}{+108} & = & \color{red}{-225x} +35 \\\Leftrightarrow & -540x \color{red}{+108} \color{blue}{-108} \color{blue}{+225x} & = & \color{red}{-225x} +35 \color{blue}{+225x} \color{blue}{-108} \\\Leftrightarrow & -540x+225x& = & 35-108 \\\Leftrightarrow & \color{red}{-315} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{-315} & & \\\Leftrightarrow & x = \frac{73}{315} & & \\ & V = \left\{ \frac{73}{315} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{4}{5})& = & 7x+\frac{9}{4} \\\Leftrightarrow & -30x-\frac{24}{5}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-600}{ \color{blue}{20} }x- \frac{96}{ \color{blue}{20} })& = & (\frac{140}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -600x \color{red}{-96} & = & \color{red}{140x} +45 \\\Leftrightarrow & -600x \color{red}{-96} \color{blue}{+96} \color{blue}{-140x} & = & \color{red}{140x} +45 \color{blue}{-140x} \color{blue}{+96} \\\Leftrightarrow & -600x-140x& = & 45+96 \\\Leftrightarrow & \color{red}{-740} x& = & 141 \\\Leftrightarrow & x = \frac{141}{-740} & & \\\Leftrightarrow & x = \frac{-141}{740} & & \\ & V = \left\{ \frac{-141}{740} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{5}{4})& = & -7x+\frac{6}{11} \\\Leftrightarrow & 9x-\frac{15}{4}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{396}{ \color{blue}{44} }x- \frac{165}{ \color{blue}{44} })& = & (\frac{-308}{ \color{blue}{44} }x+ \frac{24}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 396x \color{red}{-165} & = & \color{red}{-308x} +24 \\\Leftrightarrow & 396x \color{red}{-165} \color{blue}{+165} \color{blue}{+308x} & = & \color{red}{-308x} +24 \color{blue}{+308x} \color{blue}{+165} \\\Leftrightarrow & 396x+308x& = & 24+165 \\\Leftrightarrow & \color{red}{704} x& = & 189 \\\Leftrightarrow & x = \frac{189}{704} & & \\ & V = \left\{ \frac{189}{704} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{5}{11})& = & 9x+\frac{9}{8} \\\Leftrightarrow & 28x+\frac{35}{11}& = & 9x+\frac{9}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{2464}{ \color{blue}{88} }x+ \frac{280}{ \color{blue}{88} })& = & (\frac{792}{ \color{blue}{88} }x+ \frac{99}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 2464x \color{red}{+280} & = & \color{red}{792x} +99 \\\Leftrightarrow & 2464x \color{red}{+280} \color{blue}{-280} \color{blue}{-792x} & = & \color{red}{792x} +99 \color{blue}{-792x} \color{blue}{-280} \\\Leftrightarrow & 2464x-792x& = & 99-280 \\\Leftrightarrow & \color{red}{1672} x& = & -181 \\\Leftrightarrow & x = \frac{-181}{1672} & & \\ & V = \left\{ \frac{-181}{1672} \right\} & \\\end{align}\)