Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{3}{5})& = & -9x+\frac{3}{2} \\\Leftrightarrow & 16x-\frac{12}{5}& = & -9x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{160}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-90}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 160x \color{red}{-24} & = & \color{red}{-90x} +15 \\\Leftrightarrow & 160x \color{red}{-24} \color{blue}{+24} \color{blue}{+90x} & = & \color{red}{-90x} +15 \color{blue}{+90x} \color{blue}{+24} \\\Leftrightarrow & 160x+90x& = & 15+24 \\\Leftrightarrow & \color{red}{250} x& = & 39 \\\Leftrightarrow & x = \frac{39}{250} & & \\ & V = \left\{ \frac{39}{250} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{5}{6})& = & 5x+\frac{10}{9} \\\Leftrightarrow & 28x+\frac{35}{6}& = & 5x+\frac{10}{9} \\ & & & \text{kgv van noemers 6 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{504}{ \color{blue}{18} }x+ \frac{105}{ \color{blue}{18} })& = & (\frac{90}{ \color{blue}{18} }x+ \frac{20}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 504x \color{red}{+105} & = & \color{red}{90x} +20 \\\Leftrightarrow & 504x \color{red}{+105} \color{blue}{-105} \color{blue}{-90x} & = & \color{red}{90x} +20 \color{blue}{-90x} \color{blue}{-105} \\\Leftrightarrow & 504x-90x& = & 20-105 \\\Leftrightarrow & \color{red}{414} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{414} & & \\ & V = \left\{ \frac{-85}{414} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{3}{4})& = & -7x+\frac{3}{11} \\\Leftrightarrow & -10x+\frac{15}{4}& = & -7x+\frac{3}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-440}{ \color{blue}{44} }x+ \frac{165}{ \color{blue}{44} })& = & (\frac{-308}{ \color{blue}{44} }x+ \frac{12}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -440x \color{red}{+165} & = & \color{red}{-308x} +12 \\\Leftrightarrow & -440x \color{red}{+165} \color{blue}{-165} \color{blue}{+308x} & = & \color{red}{-308x} +12 \color{blue}{+308x} \color{blue}{-165} \\\Leftrightarrow & -440x+308x& = & 12-165 \\\Leftrightarrow & \color{red}{-132} x& = & -153 \\\Leftrightarrow & x = \frac{-153}{-132} & & \\\Leftrightarrow & x = \frac{51}{44} & & \\ & V = \left\{ \frac{51}{44} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{5}{4})& = & 8x+\frac{7}{5} \\\Leftrightarrow & 15x+\frac{15}{4}& = & 8x+\frac{7}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{300}{ \color{blue}{20} }x+ \frac{75}{ \color{blue}{20} })& = & (\frac{160}{ \color{blue}{20} }x+ \frac{28}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 300x \color{red}{+75} & = & \color{red}{160x} +28 \\\Leftrightarrow & 300x \color{red}{+75} \color{blue}{-75} \color{blue}{-160x} & = & \color{red}{160x} +28 \color{blue}{-160x} \color{blue}{-75} \\\Leftrightarrow & 300x-160x& = & 28-75 \\\Leftrightarrow & \color{red}{140} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{140} & & \\ & V = \left\{ \frac{-47}{140} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{2}{3})& = & 5x+\frac{4}{7} \\\Leftrightarrow & 8x+\frac{8}{3}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{+56} & = & \color{red}{105x} +12 \\\Leftrightarrow & 168x \color{red}{+56} \color{blue}{-56} \color{blue}{-105x} & = & \color{red}{105x} +12 \color{blue}{-105x} \color{blue}{-56} \\\Leftrightarrow & 168x-105x& = & 12-56 \\\Leftrightarrow & \color{red}{63} x& = & -44 \\\Leftrightarrow & x = \frac{-44}{63} & & \\ & V = \left\{ \frac{-44}{63} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{3}{8})& = & 4x+\frac{6}{5} \\\Leftrightarrow & 21x+\frac{21}{8}& = & 4x+\frac{6}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{840}{ \color{blue}{40} }x+ \frac{105}{ \color{blue}{40} })& = & (\frac{160}{ \color{blue}{40} }x+ \frac{48}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 840x \color{red}{+105} & = & \color{red}{160x} +48 \\\Leftrightarrow & 840x \color{red}{+105} \color{blue}{-105} \color{blue}{-160x} & = & \color{red}{160x} +48 \color{blue}{-160x} \color{blue}{-105} \\\Leftrightarrow & 840x-160x& = & 48-105 \\\Leftrightarrow & \color{red}{680} x& = & -57 \\\Leftrightarrow & x = \frac{-57}{680} & & \\ & V = \left\{ \frac{-57}{680} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{5}{8})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 12x+\frac{15}{8}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1056}{ \color{blue}{88} }x+ \frac{165}{ \color{blue}{88} })& = & (\frac{440}{ \color{blue}{88} }x+ \frac{48}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1056x \color{red}{+165} & = & \color{red}{440x} +48 \\\Leftrightarrow & 1056x \color{red}{+165} \color{blue}{-165} \color{blue}{-440x} & = & \color{red}{440x} +48 \color{blue}{-440x} \color{blue}{-165} \\\Leftrightarrow & 1056x-440x& = & 48-165 \\\Leftrightarrow & \color{red}{616} x& = & -117 \\\Leftrightarrow & x = \frac{-117}{616} & & \\ & V = \left\{ \frac{-117}{616} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{3}{4})& = & 8x+\frac{10}{3} \\\Leftrightarrow & -15x+\frac{15}{4}& = & 8x+\frac{10}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-180}{ \color{blue}{12} }x+ \frac{45}{ \color{blue}{12} })& = & (\frac{96}{ \color{blue}{12} }x+ \frac{40}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -180x \color{red}{+45} & = & \color{red}{96x} +40 \\\Leftrightarrow & -180x \color{red}{+45} \color{blue}{-45} \color{blue}{-96x} & = & \color{red}{96x} +40 \color{blue}{-96x} \color{blue}{-45} \\\Leftrightarrow & -180x-96x& = & 40-45 \\\Leftrightarrow & \color{red}{-276} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-276} & & \\\Leftrightarrow & x = \frac{5}{276} & & \\ & V = \left\{ \frac{5}{276} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{2}{11})& = & -9x+\frac{7}{8} \\\Leftrightarrow & 10x-\frac{10}{11}& = & -9x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{880}{ \color{blue}{88} }x- \frac{80}{ \color{blue}{88} })& = & (\frac{-792}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 880x \color{red}{-80} & = & \color{red}{-792x} +77 \\\Leftrightarrow & 880x \color{red}{-80} \color{blue}{+80} \color{blue}{+792x} & = & \color{red}{-792x} +77 \color{blue}{+792x} \color{blue}{+80} \\\Leftrightarrow & 880x+792x& = & 77+80 \\\Leftrightarrow & \color{red}{1672} x& = & 157 \\\Leftrightarrow & x = \frac{157}{1672} & & \\ & V = \left\{ \frac{157}{1672} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{3}{11})& = & 7x+\frac{9}{4} \\\Leftrightarrow & -30x+\frac{18}{11}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-1320}{ \color{blue}{44} }x+ \frac{72}{ \color{blue}{44} })& = & (\frac{308}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -1320x \color{red}{+72} & = & \color{red}{308x} +99 \\\Leftrightarrow & -1320x \color{red}{+72} \color{blue}{-72} \color{blue}{-308x} & = & \color{red}{308x} +99 \color{blue}{-308x} \color{blue}{-72} \\\Leftrightarrow & -1320x-308x& = & 99-72 \\\Leftrightarrow & \color{red}{-1628} x& = & 27 \\\Leftrightarrow & x = \frac{27}{-1628} & & \\\Leftrightarrow & x = \frac{-27}{1628} & & \\ & V = \left\{ \frac{-27}{1628} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{3}{8})& = & -3x+\frac{2}{3} \\\Leftrightarrow & -14x-\frac{21}{8}& = & -3x+\frac{2}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-336}{ \color{blue}{24} }x- \frac{63}{ \color{blue}{24} })& = & (\frac{-72}{ \color{blue}{24} }x+ \frac{16}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -336x \color{red}{-63} & = & \color{red}{-72x} +16 \\\Leftrightarrow & -336x \color{red}{-63} \color{blue}{+63} \color{blue}{+72x} & = & \color{red}{-72x} +16 \color{blue}{+72x} \color{blue}{+63} \\\Leftrightarrow & -336x+72x& = & 16+63 \\\Leftrightarrow & \color{red}{-264} x& = & 79 \\\Leftrightarrow & x = \frac{79}{-264} & & \\\Leftrightarrow & x = \frac{-79}{264} & & \\ & V = \left\{ \frac{-79}{264} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{4}{5})& = & 7x+\frac{4}{11} \\\Leftrightarrow & -30x+\frac{24}{5}& = & 7x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1650}{ \color{blue}{55} }x+ \frac{264}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1650x \color{red}{+264} & = & \color{red}{385x} +20 \\\Leftrightarrow & -1650x \color{red}{+264} \color{blue}{-264} \color{blue}{-385x} & = & \color{red}{385x} +20 \color{blue}{-385x} \color{blue}{-264} \\\Leftrightarrow & -1650x-385x& = & 20-264 \\\Leftrightarrow & \color{red}{-2035} x& = & -244 \\\Leftrightarrow & x = \frac{-244}{-2035} & & \\\Leftrightarrow & x = \frac{244}{2035} & & \\ & V = \left\{ \frac{244}{2035} \right\} & \\\end{align}\)