Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{2}{3})& = & -9x+\frac{7}{2} \\\Leftrightarrow & -8x+\frac{8}{3}& = & -9x+\frac{7}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-48}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{21}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -48x \color{red}{+16} & = & \color{red}{-54x} +21 \\\Leftrightarrow & -48x \color{red}{+16} \color{blue}{-16} \color{blue}{+54x} & = & \color{red}{-54x} +21 \color{blue}{+54x} \color{blue}{-16} \\\Leftrightarrow & -48x+54x& = & 21-16 \\\Leftrightarrow & \color{red}{6} x& = & 5 \\\Leftrightarrow & x = \frac{5}{6} & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{4}{9})& = & -3x+\frac{6}{11} \\\Leftrightarrow & 8x+\frac{8}{9}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{792}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} })& = & (\frac{-297}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 792x \color{red}{+88} & = & \color{red}{-297x} +54 \\\Leftrightarrow & 792x \color{red}{+88} \color{blue}{-88} \color{blue}{+297x} & = & \color{red}{-297x} +54 \color{blue}{+297x} \color{blue}{-88} \\\Leftrightarrow & 792x+297x& = & 54-88 \\\Leftrightarrow & \color{red}{1089} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{1089} & & \\ & V = \left\{ \frac{-34}{1089} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{5}{3})& = & 3x+\frac{8}{11} \\\Leftrightarrow & 8x-\frac{20}{3}& = & 3x+\frac{8}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{264}{ \color{blue}{33} }x- \frac{220}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 264x \color{red}{-220} & = & \color{red}{99x} +24 \\\Leftrightarrow & 264x \color{red}{-220} \color{blue}{+220} \color{blue}{-99x} & = & \color{red}{99x} +24 \color{blue}{-99x} \color{blue}{+220} \\\Leftrightarrow & 264x-99x& = & 24+220 \\\Leftrightarrow & \color{red}{165} x& = & 244 \\\Leftrightarrow & x = \frac{244}{165} & & \\ & V = \left\{ \frac{244}{165} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{4}{3})& = & -5x+\frac{8}{3} \\\Leftrightarrow & 12x+\frac{16}{3}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{36}{ \color{blue}{3} }x+ \frac{16}{ \color{blue}{3} })& = & (\frac{-15}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 36x \color{red}{+16} & = & \color{red}{-15x} +8 \\\Leftrightarrow & 36x \color{red}{+16} \color{blue}{-16} \color{blue}{+15x} & = & \color{red}{-15x} +8 \color{blue}{+15x} \color{blue}{-16} \\\Leftrightarrow & 36x+15x& = & 8-16 \\\Leftrightarrow & \color{red}{51} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{51} & & \\ & V = \left\{ \frac{-8}{51} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{5}{7})& = & -7x+\frac{4}{7} \\\Leftrightarrow & -6x-\frac{10}{7}& = & -7x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-42}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -42x \color{red}{-10} & = & \color{red}{-49x} +4 \\\Leftrightarrow & -42x \color{red}{-10} \color{blue}{+10} \color{blue}{+49x} & = & \color{red}{-49x} +4 \color{blue}{+49x} \color{blue}{+10} \\\Leftrightarrow & -42x+49x& = & 4+10 \\\Leftrightarrow & \color{red}{7} x& = & 14 \\\Leftrightarrow & x = \frac{14}{7} & & \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{5}{8})& = & 4x+\frac{4}{3} \\\Leftrightarrow & 9x+\frac{15}{8}& = & 4x+\frac{4}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{216}{ \color{blue}{24} }x+ \frac{45}{ \color{blue}{24} })& = & (\frac{96}{ \color{blue}{24} }x+ \frac{32}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 216x \color{red}{+45} & = & \color{red}{96x} +32 \\\Leftrightarrow & 216x \color{red}{+45} \color{blue}{-45} \color{blue}{-96x} & = & \color{red}{96x} +32 \color{blue}{-96x} \color{blue}{-45} \\\Leftrightarrow & 216x-96x& = & 32-45 \\\Leftrightarrow & \color{red}{120} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{120} & & \\ & V = \left\{ \frac{-13}{120} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{3}{7})& = & -7x+\frac{3}{4} \\\Leftrightarrow & -6x+\frac{6}{7}& = & -7x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-168}{ \color{blue}{28} }x+ \frac{24}{ \color{blue}{28} })& = & (\frac{-196}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -168x \color{red}{+24} & = & \color{red}{-196x} +21 \\\Leftrightarrow & -168x \color{red}{+24} \color{blue}{-24} \color{blue}{+196x} & = & \color{red}{-196x} +21 \color{blue}{+196x} \color{blue}{-24} \\\Leftrightarrow & -168x+196x& = & 21-24 \\\Leftrightarrow & \color{red}{28} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{28} & & \\ & V = \left\{ \frac{-3}{28} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{3}{4})& = & -7x+\frac{3}{7} \\\Leftrightarrow & 25x-\frac{15}{4}& = & -7x+\frac{3}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{700}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{-196}{ \color{blue}{28} }x+ \frac{12}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 700x \color{red}{-105} & = & \color{red}{-196x} +12 \\\Leftrightarrow & 700x \color{red}{-105} \color{blue}{+105} \color{blue}{+196x} & = & \color{red}{-196x} +12 \color{blue}{+196x} \color{blue}{+105} \\\Leftrightarrow & 700x+196x& = & 12+105 \\\Leftrightarrow & \color{red}{896} x& = & 117 \\\Leftrightarrow & x = \frac{117}{896} & & \\ & V = \left\{ \frac{117}{896} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{5}{7})& = & -4x+\frac{3}{11} \\\Leftrightarrow & -18x+\frac{30}{7}& = & -4x+\frac{3}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1386}{ \color{blue}{77} }x+ \frac{330}{ \color{blue}{77} })& = & (\frac{-308}{ \color{blue}{77} }x+ \frac{21}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1386x \color{red}{+330} & = & \color{red}{-308x} +21 \\\Leftrightarrow & -1386x \color{red}{+330} \color{blue}{-330} \color{blue}{+308x} & = & \color{red}{-308x} +21 \color{blue}{+308x} \color{blue}{-330} \\\Leftrightarrow & -1386x+308x& = & 21-330 \\\Leftrightarrow & \color{red}{-1078} x& = & -309 \\\Leftrightarrow & x = \frac{-309}{-1078} & & \\\Leftrightarrow & x = \frac{309}{1078} & & \\ & V = \left\{ \frac{309}{1078} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{4}{7})& = & 5x+\frac{9}{4} \\\Leftrightarrow & -12x-\frac{16}{7}& = & 5x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-336}{ \color{blue}{28} }x- \frac{64}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -336x \color{red}{-64} & = & \color{red}{140x} +63 \\\Leftrightarrow & -336x \color{red}{-64} \color{blue}{+64} \color{blue}{-140x} & = & \color{red}{140x} +63 \color{blue}{-140x} \color{blue}{+64} \\\Leftrightarrow & -336x-140x& = & 63+64 \\\Leftrightarrow & \color{red}{-476} x& = & 127 \\\Leftrightarrow & x = \frac{127}{-476} & & \\\Leftrightarrow & x = \frac{-127}{476} & & \\ & V = \left\{ \frac{-127}{476} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{5}{7})& = & 7x+\frac{3}{2} \\\Leftrightarrow & 30x-\frac{30}{7}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{420}{ \color{blue}{14} }x- \frac{60}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 420x \color{red}{-60} & = & \color{red}{98x} +21 \\\Leftrightarrow & 420x \color{red}{-60} \color{blue}{+60} \color{blue}{-98x} & = & \color{red}{98x} +21 \color{blue}{-98x} \color{blue}{+60} \\\Leftrightarrow & 420x-98x& = & 21+60 \\\Leftrightarrow & \color{red}{322} x& = & 81 \\\Leftrightarrow & x = \frac{81}{322} & & \\ & V = \left\{ \frac{81}{322} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{5}{4})& = & -4x+\frac{6}{5} \\\Leftrightarrow & -15x+\frac{15}{4}& = & -4x+\frac{6}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-300}{ \color{blue}{20} }x+ \frac{75}{ \color{blue}{20} })& = & (\frac{-80}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -300x \color{red}{+75} & = & \color{red}{-80x} +24 \\\Leftrightarrow & -300x \color{red}{+75} \color{blue}{-75} \color{blue}{+80x} & = & \color{red}{-80x} +24 \color{blue}{+80x} \color{blue}{-75} \\\Leftrightarrow & -300x+80x& = & 24-75 \\\Leftrightarrow & \color{red}{-220} x& = & -51 \\\Leftrightarrow & x = \frac{-51}{-220} & & \\\Leftrightarrow & x = \frac{51}{220} & & \\ & V = \left\{ \frac{51}{220} \right\} & \\\end{align}\)