Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{2}{5})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -30x-\frac{12}{5}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-450}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -450x \color{red}{-36} & = & \color{red}{105x} +40 \\\Leftrightarrow & -450x \color{red}{-36} \color{blue}{+36} \color{blue}{-105x} & = & \color{red}{105x} +40 \color{blue}{-105x} \color{blue}{+36} \\\Leftrightarrow & -450x-105x& = & 40+36 \\\Leftrightarrow & \color{red}{-555} x& = & 76 \\\Leftrightarrow & x = \frac{76}{-555} & & \\\Leftrightarrow & x = \frac{-76}{555} & & \\ & V = \left\{ \frac{-76}{555} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{2}{5})& = & 7x+\frac{5}{2} \\\Leftrightarrow & 16x+\frac{8}{5}& = & 7x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{160}{ \color{blue}{10} }x+ \frac{16}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 160x \color{red}{+16} & = & \color{red}{70x} +25 \\\Leftrightarrow & 160x \color{red}{+16} \color{blue}{-16} \color{blue}{-70x} & = & \color{red}{70x} +25 \color{blue}{-70x} \color{blue}{-16} \\\Leftrightarrow & 160x-70x& = & 25-16 \\\Leftrightarrow & \color{red}{90} x& = & 9 \\\Leftrightarrow & x = \frac{9}{90} & & \\\Leftrightarrow & x = \frac{1}{10} & & \\ & V = \left\{ \frac{1}{10} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{4}{11})& = & 3x+\frac{7}{2} \\\Leftrightarrow & -28x-\frac{28}{11}& = & 3x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-616}{ \color{blue}{22} }x- \frac{56}{ \color{blue}{22} })& = & (\frac{66}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -616x \color{red}{-56} & = & \color{red}{66x} +77 \\\Leftrightarrow & -616x \color{red}{-56} \color{blue}{+56} \color{blue}{-66x} & = & \color{red}{66x} +77 \color{blue}{-66x} \color{blue}{+56} \\\Leftrightarrow & -616x-66x& = & 77+56 \\\Leftrightarrow & \color{red}{-682} x& = & 133 \\\Leftrightarrow & x = \frac{133}{-682} & & \\\Leftrightarrow & x = \frac{-133}{682} & & \\ & V = \left\{ \frac{-133}{682} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{2}{7})& = & 6x+\frac{8}{5} \\\Leftrightarrow & 25x+\frac{10}{7}& = & 6x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{875}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} })& = & (\frac{210}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 875x \color{red}{+50} & = & \color{red}{210x} +56 \\\Leftrightarrow & 875x \color{red}{+50} \color{blue}{-50} \color{blue}{-210x} & = & \color{red}{210x} +56 \color{blue}{-210x} \color{blue}{-50} \\\Leftrightarrow & 875x-210x& = & 56-50 \\\Leftrightarrow & \color{red}{665} x& = & 6 \\\Leftrightarrow & x = \frac{6}{665} & & \\ & V = \left\{ \frac{6}{665} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{3}{7})& = & 3x+\frac{3}{4} \\\Leftrightarrow & 8x+\frac{6}{7}& = & 3x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{224}{ \color{blue}{28} }x+ \frac{24}{ \color{blue}{28} })& = & (\frac{84}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 224x \color{red}{+24} & = & \color{red}{84x} +21 \\\Leftrightarrow & 224x \color{red}{+24} \color{blue}{-24} \color{blue}{-84x} & = & \color{red}{84x} +21 \color{blue}{-84x} \color{blue}{-24} \\\Leftrightarrow & 224x-84x& = & 21-24 \\\Leftrightarrow & \color{red}{140} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{140} & & \\ & V = \left\{ \frac{-3}{140} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{4}{11})& = & -9x+\frac{9}{4} \\\Leftrightarrow & -8x-\frac{16}{11}& = & -9x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-352}{ \color{blue}{44} }x- \frac{64}{ \color{blue}{44} })& = & (\frac{-396}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -352x \color{red}{-64} & = & \color{red}{-396x} +99 \\\Leftrightarrow & -352x \color{red}{-64} \color{blue}{+64} \color{blue}{+396x} & = & \color{red}{-396x} +99 \color{blue}{+396x} \color{blue}{+64} \\\Leftrightarrow & -352x+396x& = & 99+64 \\\Leftrightarrow & \color{red}{44} x& = & 163 \\\Leftrightarrow & x = \frac{163}{44} & & \\ & V = \left\{ \frac{163}{44} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{5}{3})& = & -7x+\frac{10}{9} \\\Leftrightarrow & -16x-\frac{20}{3}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-144}{ \color{blue}{9} }x- \frac{60}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -144x \color{red}{-60} & = & \color{red}{-63x} +10 \\\Leftrightarrow & -144x \color{red}{-60} \color{blue}{+60} \color{blue}{+63x} & = & \color{red}{-63x} +10 \color{blue}{+63x} \color{blue}{+60} \\\Leftrightarrow & -144x+63x& = & 10+60 \\\Leftrightarrow & \color{red}{-81} x& = & 70 \\\Leftrightarrow & x = \frac{70}{-81} & & \\\Leftrightarrow & x = \frac{-70}{81} & & \\ & V = \left\{ \frac{-70}{81} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{2}{3})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -10x+\frac{10}{3}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-150}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -150x \color{red}{+50} & = & \color{red}{-105x} +18 \\\Leftrightarrow & -150x \color{red}{+50} \color{blue}{-50} \color{blue}{+105x} & = & \color{red}{-105x} +18 \color{blue}{+105x} \color{blue}{-50} \\\Leftrightarrow & -150x+105x& = & 18-50 \\\Leftrightarrow & \color{red}{-45} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{-45} & & \\\Leftrightarrow & x = \frac{32}{45} & & \\ & V = \left\{ \frac{32}{45} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{4}{11})& = & -5x+\frac{3}{2} \\\Leftrightarrow & 24x+\frac{24}{11}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{528}{ \color{blue}{22} }x+ \frac{48}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 528x \color{red}{+48} & = & \color{red}{-110x} +33 \\\Leftrightarrow & 528x \color{red}{+48} \color{blue}{-48} \color{blue}{+110x} & = & \color{red}{-110x} +33 \color{blue}{+110x} \color{blue}{-48} \\\Leftrightarrow & 528x+110x& = & 33-48 \\\Leftrightarrow & \color{red}{638} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{638} & & \\ & V = \left\{ \frac{-15}{638} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{5}{7})& = & -5x+\frac{10}{3} \\\Leftrightarrow & -9x-\frac{15}{7}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-189}{ \color{blue}{21} }x- \frac{45}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -189x \color{red}{-45} & = & \color{red}{-105x} +70 \\\Leftrightarrow & -189x \color{red}{-45} \color{blue}{+45} \color{blue}{+105x} & = & \color{red}{-105x} +70 \color{blue}{+105x} \color{blue}{+45} \\\Leftrightarrow & -189x+105x& = & 70+45 \\\Leftrightarrow & \color{red}{-84} x& = & 115 \\\Leftrightarrow & x = \frac{115}{-84} & & \\\Leftrightarrow & x = \frac{-115}{84} & & \\ & V = \left\{ \frac{-115}{84} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{4}{5})& = & 5x+\frac{3}{7} \\\Leftrightarrow & 12x+\frac{12}{5}& = & 5x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+84} & = & \color{red}{175x} +15 \\\Leftrightarrow & 420x \color{red}{+84} \color{blue}{-84} \color{blue}{-175x} & = & \color{red}{175x} +15 \color{blue}{-175x} \color{blue}{-84} \\\Leftrightarrow & 420x-175x& = & 15-84 \\\Leftrightarrow & \color{red}{245} x& = & -69 \\\Leftrightarrow & x = \frac{-69}{245} & & \\ & V = \left\{ \frac{-69}{245} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{5}{4})& = & 4x+\frac{2}{9} \\\Leftrightarrow & 9x-\frac{15}{4}& = & 4x+\frac{2}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{324}{ \color{blue}{36} }x- \frac{135}{ \color{blue}{36} })& = & (\frac{144}{ \color{blue}{36} }x+ \frac{8}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 324x \color{red}{-135} & = & \color{red}{144x} +8 \\\Leftrightarrow & 324x \color{red}{-135} \color{blue}{+135} \color{blue}{-144x} & = & \color{red}{144x} +8 \color{blue}{-144x} \color{blue}{+135} \\\Leftrightarrow & 324x-144x& = & 8+135 \\\Leftrightarrow & \color{red}{180} x& = & 143 \\\Leftrightarrow & x = \frac{143}{180} & & \\ & V = \left\{ \frac{143}{180} \right\} & \\\end{align}\)